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Simple Extensions with the Minimum Degree Relations of Integral Domains

Simple Extensions with the Minimum Degree Relations of Integral Domains

Although there are many types of ring extensions simple extensions have yet to be thoroughly explored in one book. Covering an understudied aspect of commutative algebra Simple Extensions with the Minimum Degree Relations of Integral Domains presents a comprehensive treatment of various simple extensions and their properties. In particular it examines several properties of simple ring extensions of Noetherian integral domains. As experts who have been studying this field for over a decade the authors present many arguments that they have developed themselves mainly exploring anti-integral super-primitive and ultra-primitive extensions. Within this framework they study certain properties such as flatness integrality and unramifiedness. Some of the topics discussed include Sharma polynomials vanishing points Noetherian domains denominator ideals unit groups and polynomial rings. Presenting a complete treatment of each topic Simple Extensions with the Minimum Degree Relations of Integral Domains serves as an ideal resource for graduate students and researchers involved in the area of commutative algebra.

GBP 180.00
1

Direct Sum Decompositions of Torsion-Free Finite Rank Groups

Direct Sum Decompositions of Torsion-Free Finite Rank Groups

With plenty of new material not found in other books Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups. Offering a unified approach to theoretic concepts this reference covers isomorphism endomorphism refinement the Baer splitting property Gabriel filters and endomorphism modules. It shows how to effectively study a group G by considering finitely generated projective right End(G)-modules the left End(G)-module G and the ring E(G) = End(G)/N(End(G)). For instance one of the naturally occurring properties considered is when E(G) is a commutative ring. Modern algebraic number theory provides results concerning the isomorphism of locally isomorphic rtffr groups finitely faithful S-groups that are J-groups and each rtffr L-group that is a J-group. The book concludes with useful appendices that contain background material and numerous examples.

GBP 59.99
1

Parallel Algorithms

Parallel Algorithms

Focusing on algorithms for distributed-memory parallel architectures Parallel Algorithms presents a rigorous yet accessible treatment of theoretical models of parallel computation parallel algorithm design for homogeneous and heterogeneous platforms complexity and performance analysis and essential notions of scheduling. The book extracts fundamental ideas and algorithmic principles from the mass of parallel algorithm expertise and practical implementations developed over the last few decades. In the first section of the text the authors cover two classical theoretical models of parallel computation (PRAMs and sorting networks) describe network models for topology and performance and define several classical communication primitives. The next part deals with parallel algorithms on ring and grid logical topologies as well as the issue of load balancing on heterogeneous computing platforms. The final section presents basic results and approaches for common scheduling problems that arise when developing parallel algorithms. It also discusses advanced scheduling topics such as divisible load scheduling and steady-state scheduling. With numerous examples and exercises in each chapter this text encompasses both the theoretical foundations of parallel algorithms and practical parallel algorithm design.

GBP 44.99
1

Student Solutions Manual for Gallian's Contemporary Abstract Algebra

Student Solutions Manual for Gallian's Contemporary Abstract Algebra

Whereas many partial solutions and sketches for the odd-numbered exercises appear in the book the Student Solutions Manual written by the author has comprehensive solutions for all odd-numbered exercises and large number of even-numbered exercises. This Manual also offers many alternative solutions to those appearing in the text. These will provide the student with a better understanding of the material. This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra Tenth Edition and is designed to supplement that text. Table of Contents Integers and Equivalence Relations0. Preliminaries Groups1. Introduction to Groups 2. Groups 3. Finite Groups; Subgroups 4. Cyclic Groups 5. Permutation Groups 6. Isomorphisms 7. Cosets and Lagrange's Theorem 8. External Direct Products 9. Normal Subgroups and Factor Groups 10. Group Homomorphisms 11. Fundamental Theorem of Finite Abelian Groups Rings12. Introduction to Rings 13. Integral Domains14. Ideals and Factor Rings 15. Ring Homomorphisms 16. Polynomial Rings 17. Factorization of Polynomials 18. Divisibility in Integral Domains FieldsFields19. Extension Fields 20. Algebraic Extensions21. Finite Fields 22. Geometric Constructions Special Topics23. Sylow Theorems 24. Finite Simple Groups 25. Generators and Relations 26. Symmetry Groups 27. Symmetry and Counting 28. Cayley Digraphs of Groups 29. Introduction to Algebraic Coding Theory 30. An Introduction to Galois Theory 31. Cyclotomic Extensions Biography Joseph A. Gallian earned his PhD from Notre Dame. In addition to receiving numerous national awards for his teaching and exposition he has served terms as the Second Vice President and the President of the MAA. He has served on 40 national committees chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in the national news outlets including the New York Times the Washington Post the Boston Globe and Newsweek among many others. | Student Solutions Manual for Gallian's Contemporary Abstract Algebra

GBP 44.99
1