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Aljadeff and colleagues explore the idea of an identity in an algebraic structure, defining such an identity as a symbolic expression involving one or several operations and one or several variables, which is identically satisfied when the variables are substituted in a given algebraic structure. Here they restrict their treatment to a special type of identities, satisfied by associative algebras, over some commutative ring A. They take as symbolic expressions the non-commutative polynomials, with coefficients in A, in some finite or infinite set of variables. Annotation ©2021 Ringgold, Inc., Portland, OR (protoview.com)
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Rings With Polynomial Identities and Finite Dimensional Representations of Algebras
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American Mathematical Society, 2020
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ISBN 13: 9781470451745
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Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
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American Mathematical Society, 2020
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Condizione: New. A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study i. Codice articolo 595975379
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Rings With Polynomial Identities and Finite Dimensional Representations of Algebras
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Hardcover. Condizione: Brand New. 630 pages. 10.25x7.25x1.50 inches. In Stock. Codice articolo __1470451743
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Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
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MP-AMM American Mathematical, 2020
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Rings With Polynomial Identities and Finite Dimensional Representations of Algebras
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American Mathematical Society, 2020
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Rings With Polynomial Identities and Finite Dimensional Representations of Algebras
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American Mathematical Society, 2020
ISBN 10: 1470451743
ISBN 13: 9781470451745
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Rings With Polynomial Identities and Finite Dimensional Representations of Algebras
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American Mathematical Society, 2020
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Rings with Polynomial Identities and Finite Dimensional Representations of Algebras (Colloquium Publications)
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American Mathematical Society, 2020
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Rings with Polynomial Identities and Finite Dimensional Representations of Algebras (Colloquium Publications)
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American Mathematical Society, 2020
ISBN 10: 1470451743
ISBN 13: 9781470451745
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Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
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American Mathematical Society, US, 2020
ISBN 10: 1470451743
ISBN 13: 9781470451745
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Paperback. Condizione: New. A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley-Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem. Codice articolo LU-9781470451745
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