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Topics in Commutative Ring Theory - John J. Watkins - Bog - Princeton University Press - Plusbog.dk

Topics in Commutative Ring Theory - John J. Watkins - Bog - Princeton University Press - Plusbog.dk

Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra. Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat''s last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics. Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study.

DKK 935.00
1

Chow Rings, Decomposition of the Diagonal, and the Topology of Families - Claire Voisin - Bog - Princeton University Press - Plusbog.dk

Chow Rings, Decomposition of the Diagonal, and the Topology of Families - Claire Voisin - Bog - Princeton University Press - Plusbog.dk

In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by Voisin. The book focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by Voisin looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori''s work that have been further developed by others.

DKK 693.00
1

Continuous Geometry - John Von Neumann - Bog - Princeton University Press - Plusbog.dk

Continuous Geometry - John Von Neumann - Bog - Princeton University Press - Plusbog.dk

In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln . In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann''s lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, and--for the irreducible case--the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.

DKK 854.00
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The Notebooks - Jean Michel Basquiat - Bog - Princeton University Press - Plusbog.dk

The Notebooks - Jean Michel Basquiat - Bog - Princeton University Press - Plusbog.dk

A facsimile edition of the artist''s fascinating working notebooks Brooklyn-born Jean-Michel Basquiat (1960-88) was one of the most important artists of the 1980s. A key figure in the New York art scene, he inventively explored the interplay between words and images throughout his career, first as a member of SAMO, a graffiti group active on the Lower East Side in the late 1970s, and then as a painter acclaimed for his unmistakable Neoexpressionist style. From 1980 to 1987, he filled numerous working notebooks with drawings and handwritten texts. This facsimile edition reproduces the pages of eight of these fascinating and rarely seen notebooks for the first time.The notebooks are filled with images and words that recur in Basquiat''s paintings and other works. Iconic drawings and pictograms of crowns, teepees, and hatch-marked hearts share space with handwritten texts, including notes, observations, and poems that often touch on culture, race, class, and life in New York. Like his other work, the notebooks vividly demonstrate Basquiat’s deep interests in comic, street, and pop art, hip-hop, politics, and the ephemera of urban life. They also provide an intimate look at the working process of one of the most creative forces in contemporary American art.Published in association with No More Rulers

DKK 293.00
1

Homological Algebra - Henry Cartan - Bog - Princeton University Press - Plusbog.dk

Homological Algebra - Henry Cartan - Bog - Princeton University Press - Plusbog.dk

When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.

DKK 965.00
1

Quadrangular Algebras - Richard M. Weiss - Bog - Princeton University Press - Plusbog.dk

Quadrangular Algebras - Richard M. Weiss - Bog - Princeton University Press - Plusbog.dk

This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms.

DKK 713.00
1

The Geometry and Cohomology of Some Simple Shimura Varieties - Richard Taylor - Bog - Princeton University Press - Plusbog.dk

The Geometry and Cohomology of Some Simple Shimura Varieties - Richard Taylor - Bog - Princeton University Press - Plusbog.dk

This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands''s 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n -dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory.

DKK 790.00
1

The Wagner Operas - Ernest Newman - Bog - Princeton University Press - Plusbog.dk

The Wagner Operas - Ernest Newman - Bog - Princeton University Press - Plusbog.dk

In this classic guide, the foremost Wagner expert of our century discusses ten of Wagner''s most beloved operas, illuminates their key themes and the myths and literary sources behind the librettos, and demonstrates how the composer''s style changed from work to work. Acclaimed as the most complete and intellectually satisfying analysis of the Wagner operas, the book has met with unreserved enthusiasm from specialist and casual music lover alike. Here, available for the first time in a single paperback volume, is the perfect companion for listening to, or attending, The Flying Dutchman, Tannhäuser, Lohengrin, Tristan and Isolde, Die Meistersinger, the four operas of the Ring Cycle, and Parsifal. Newman enriches his treatment of the stories, texts, and music of the operas with biographical and historical materials from the store of knowledge that he acquired while completing his numerous books on Wagner, including the magisterial Life of Richard Wagner. The text of The Wagner Operas is filled with hundreds of musical examples from the scores, and all the important leitmotifs and their interrelationships are made clear in Newman''s lucid prose. "This is as fine an introduction as any ever written about a major composer''s masterpieces. Newman outlines with unfailing clarity and astuteness each opera''s dramatic sources, and he takes the student through the completed opera, step by step, with all manner of incidental insight along the way."--Robert Bailey, New York University

DKK 309.00
1

The Shield of Homer - Keith Stanley - Bog - Princeton University Press - Plusbog.dk

The Shield of Homer - Keith Stanley - Bog - Princeton University Press - Plusbog.dk

In this masterly interpretation of narrative sequence in the Iliad , Keith Stanley not only sharpens the current debate over the date and creation of the poem, but also challenges the view of this work as primarily a celebration of heroic force. He begins by studying the intricate ring-composition in the verses describing Achilles'' shield, then extends this analysis to reveal the Iliad as an elaborate and self-conscious formal whole. In so doing he defends the hypothesis that the poem as we know it is a massive reorganization and expansion of earlier "Homeric" material, written in response to the need for a stable text for repeated performance at the sixth-century Athenian festival for the city''s patron goddess.Stanley explores the arrangement of the poem''s books, all unified by theme and structure, showing how this allowed for artistically satisfying and practically feasible recitation over a period of three or four days. Taking structural emphasis as a guide to poetic discourse, the author argues that the Iliad is not a poem of "might"--as opposed to the Odyssean celebration of "guile"--but that in advocating social and personal reconciliation the poem offers a profound indictment of a warring heroic society.Originally published in 1993.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

DKK 613.00
1

Drama and the World of Richard Wagner - Dieter Borchmeyer - Bog - Princeton University Press - Plusbog.dk

Drama and the World of Richard Wagner - Dieter Borchmeyer - Bog - Princeton University Press - Plusbog.dk

Richard Wagner continues to be the most controversial artist in history, a perpetually troubling figure in our cultural consciousness. The unceasing debate over his works and their impact--for and against--is one reason why there has been no genuinely comprehensive modern account of his musical dramas until now. Dieter Borchmeyer''s book is the first to present an overall picture of these musical dramas from the standpoint of literary and theatrical history. It extends from the composer''s early works--still largely ignored--to the Ring Cycle and Parsifal , and includes Wagner''s unfinished works and operas he never set to music. Through lively prose, we come to see Wagner as a librettist--and as a man of letters--rather than primarily as musical composer.Borchmeyer uncovers a vast field of cultural and historical cross-references in Wagner''s works. In the first part of the book, he sets out in search of the various archetypal scenes, opening up the composer''s dramatic workshop to the reader. He covers all of Wagner''s operas, from early juvenilia to the canonical later works.The second part examines Wagner in relation to political figures including King Ludwig II and Bismarck, and, importantly, in light of critical reactions by literary giants--Thomas Mann, whom Borchmeyer calls "a guiding light in this exploration of the fields that Wagner tilled," and Nietzsche, whose appeal to "philology" is a key source of inspiration in attempts to grapple with Wagner''s works.For more than twenty years, Borchmeyer has placed his scholarship at the service of the famed Bayreuth Festival. With this volume, he gives us a summation of decades of engagement with the phenomenon of Wagner and, at the same time, the result of an abiding critical passion for his works.

DKK 653.00
1

Wagner Androgyne - Jean Jacques Nattiez - Bog - Princeton University Press - Plusbog.dk

Wagner Androgyne - Jean Jacques Nattiez - Bog - Princeton University Press - Plusbog.dk

That Wagner conceived of himself creatively as both man and woman is central to an understanding of his life and art. So argues Jean-Jacques Nattiez in this richly insightful work, where he draws from semiology, music criticism, and psychoanalysis to explore such topics as Wagner''s theories of music drama, his anti-Semitism, and his psyche.Wagner, who wrote the libretti for the operas he composed, maintained that art is the union of the feminine principle, music, and the masculine principle, poetry. In light of this androgynous model, Nattiez reinterprets the Wagnerian canon, especially the Ring of the Nibelung, which is shown to contain a metaphorical transposition of Wagner''s conception of the history of music: Siegfried appears as the poet, Brunnhilde, as music, and their union is an androgynous one in which individual identity fades and the lovers revert to a preconflictual, presexual state.Nattiez traces the androgynous symbol in Wagner''s theoretical writings throughout his career. Looking to explain how this idea, so closely bound up with sexuality, took root in Wagner''s mind, the author considers the possibility of Freudian and Jungian interpretations. In particular he explores the composer''s relationship with his mother, a distant woman who discouraged his interest in the theater, and his stepfather, a loving man whom Wagner suspected was not only his real father but also a Jew. Along with psychoanalysis, Nattiez critically applies various structuralist and feminist theories to Wagner''s creative enterprise to demonstrate how the nature of twentieth-century hermeneutics is itself androgynous.Originally published in 1993.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

DKK 484.00
1