Brauer Groups and the Cohomology of Graded Rings

Author: Stefaan Caenepeel

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 280

View: 831

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.

Brauer Groups and the Cohomology of Graded Rings

Author: Caenepeel

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 280

View: 564

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.

Rings, Hopf Algebras, and Brauer Groups

Author: Stefaan Caenepeel

Publisher: CRC Press

ISBN:

Category: Mathematics

Page:

View: 322

"Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "

Brauer Groups and the Cohomology of Graded Rings

Author: Stefaan Caenepeel

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 280

View: 408

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.

Brauer Groups, Hopf Algebras and Galois Theory

Author: Stefaan Caenepeel

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 488

View: 196

This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a new self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and étale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Recent developments are considered and examples are included. The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph. Audience: Researchers whose work involves group theory. The first two parts, in particular, can be recommended for supplementary, graduate course use.

Graded Rings and Graded Grothendieck Groups

Author: Roozbeh Hazrat

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 237

View: 749

This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.

Algebra And Number Theory

Author: Mohammed Boulagouaz

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 304

View: 101

This study demonstrates the key manipulations surrounding Brauer groups, graded rings, group representations, ideal classes of number fields, p-adic differential equations, and rationality problems of invariant fields - displaying a command of the most advanced methods in algebra. It describes new developments in noncommutative valuation theory and

Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

Author: Alexander J. Hahn

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 286

View: 295

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.

Graded Orders

Author: F.M., van Oystaeyen

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 208

View: 885

In a clear, well-developed presentation this book provides the first systematic treatment of structure results for algebras which are graded by a goup. The fruitful method of constructing graded orders of special kind over a given order, culminating in applications of the construction of generalized Rees rings associated to divisors, is combined with the theory of orders over graded Krull domains. This yields the construction of generalized Rees rings corresponding to the central ramification divisor of the orders and the algebraic properties of the constructed orders. The graded methods allow the study of regularity conditions on order. The book also touches upon representation theoretic methods, including orders of finite representation type and other aspects of this theory applicable to the classification of orders. The final chapter describes the ring theoretical approach to the classification of orders of global dimension two, originally carried out by M. Artin using more geometrical methods. Since its subject is important in many research areas, this book will be valuable reading for all researchers and graduate students with an interest in non-commutative algebra.

Algebraic Geometry for Associative Algebras

Author: Freddy Van Oystaeyen

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 302

View: 593

This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theor

Brauer Groups

Proceedings of the Conference Held at Evanston, October 11-15, 1975

Author: D. Zelinsky

Publisher: Springer Verlag

ISBN:

Category: Mathematics

Page: 187

View: 501

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Rings, Hopf Algebras, and Brauer Groups

Author: Stefaan Caenepeel

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 352

View: 885

"Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "

Generalized Lie Theory in Mathematics, Physics and Beyond

Author: Sergei D. Silvestrov

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 306

View: 217

This book explores the cutting edge of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics.

Algebraic Generalizations of Discrete Groups

A Path to Combinatorial Group Theory Through One-Relator Products

Author: Benjamin Fine

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 328

View: 133

A survey of one-relator products of cyclics or groups with a single defining relation, extending the algebraic study of Fuchsian groups to the more general context of one-relator products and related group theoretical considerations. It provides a self-contained account of certain natural generalizations of discrete groups.

Semigroups

An Introduction to the Structure Theory

Author: Pierre A. Grillet

Publisher: Routledge

ISBN:

Category: Mathematics

Page: 408

View: 731

This work offers concise coverage of the structure theory of semigroups. It examines constructions and descriptions of semigroups and emphasizes finite, commutative, regular and inverse semigroups. Many structure theorems on regular and commutative semigroups are introduced.;College or university bookstores may order five or more copies at a special student price which is available upon request from Marcel Dekker, Inc.

Semigroup Algebras

Author: Jan Okninski

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 376

View: 377

Gathers and unifies the results of the theory of noncommutative semigroup rings, primarily drawing on the literature of the last 10 years, and including several new results. Okninski (Warsaw U., Poland) restricts coverage to the ring theoretical properties for which a systematic treatment is current