Brauer Groups and the Cohomology of Graded Rings

Brauer Groups and the Cohomology of Graded Rings

Author: Stefaan Caenepeel

Publisher: CRC Press

Published: 2020-08-26

Total Pages: 280

ISBN-13: 1000103781

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This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.


Methods of Graded Rings

Methods of Graded Rings

Author: Constantin Nastasescu

Publisher: Springer Science & Business Media

Published: 2004-02-19

Total Pages: 324

ISBN-13: 9783540207467

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The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A:Some Category Theory.- Appendix B: Dimensions in an abelian Category.- Bibliography.- Index.-


Hopf Algebras and Quantum Groups

Hopf Algebras and Quantum Groups

Author: Stefaan Caenepeel

Publisher: CRC Press

Published: 2019-05-07

Total Pages: 332

ISBN-13: 0429529988

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This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum g


Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

Author: Alexander J. Hahn

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 296

ISBN-13: 146846311X

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Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.


Hopf Algebras in Noncommutative Geometry and Physics

Hopf Algebras in Noncommutative Geometry and Physics

Author: Stefaan Caenepeel

Publisher: CRC Press

Published: 2019-05-07

Total Pages: 348

ISBN-13: 0429530072

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This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the


Introduction to Set Theory, Revised and Expanded

Introduction to Set Theory, Revised and Expanded

Author: Karel Hrbacek

Publisher: CRC Press

Published: 2017-12-19

Total Pages: 310

ISBN-13: 1482276852

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Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.


Inequalities for Finite Difference Equations

Inequalities for Finite Difference Equations

Author: B.G. Pachpatte

Publisher: CRC Press

Published: 2001-12-13

Total Pages: 533

ISBN-13: 1482271060

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"A treatise on finite difference ineuqalities that have important applications to theories of various classes of finite difference and sum-difference equations, including several linear and nonlinear finite difference inequalities appearing for the first time in book form."


Optimal Design of Control Systems

Optimal Design of Control Systems

Author: Gennadii E. Kolosov

Publisher: CRC Press

Published: 2020-08-26

Total Pages: 420

ISBN-13: 1000103323

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"Covers design methods for optimal (or quasioptimal) control algorithms in the form of synthesis for deterministic and stochastic dynamical systems-with applications in aerospace, robotic, and servomechanical technologies. Providing new results on exact and approximate solutions of optimal control problems."


Coding Theory and Cryptography

Coding Theory and Cryptography

Author: D.C. Hankerson

Publisher: CRC Press

Published: 2000-08-04

Total Pages: 362

ISBN-13: 1482270706

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Containing data on number theory, encryption schemes, and cyclic codes, this highly successful textbook, proven by the authors in a popular two-quarter course, presents coding theory, construction, encoding, and decoding of specific code families in an "easy-to-use" manner appropriate for students with only a basic background in mathematics offerin