Noetherian Rings and Rings with Polynomial Identities
Author:
Publisher:
Published: 1979
Total Pages: 420
ISBN-13:
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Author:
Publisher:
Published: 1979
Total Pages: 420
ISBN-13:
DOWNLOAD EBOOKAuthor: Eli Aljadeff
Publisher: American Mathematical Soc.
Published: 2020-12-14
Total Pages: 630
ISBN-13: 1470451743
DOWNLOAD EBOOKA polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A 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.
Author: Claudio Procesi
Publisher:
Published: 1973
Total Pages: 232
ISBN-13:
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Publisher: Academic Press
Published: 1980-07-24
Total Pages: 387
ISBN-13: 0080874002
DOWNLOAD EBOOKPolynomial Identities in Ring Theory
Author: Lance W. Small
Publisher:
Published: 1980
Total Pages: 48
ISBN-13:
DOWNLOAD EBOOKAuthor: Vesselin Drensky
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 197
ISBN-13: 3034879342
DOWNLOAD EBOOKThese lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject.
Author: Alexei Kanel-Belov
Publisher: CRC Press
Published: 2015-10-22
Total Pages: 436
ISBN-13: 1498720099
DOWNLOAD EBOOKComputational Aspects of Polynomial Identities: Volume l, Kemer's Theorems, 2nd Edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. This edition gives all the details involved in Kemer's proof of Specht's conjecture for affine PI-algebras in characteristic 0.The
Author: Lance W. Small
Publisher: American Mathematical Soc.
Published: 1987
Total Pages: 130
ISBN-13: 0821815253
DOWNLOAD EBOOK". T. Stafford -- The Goldie rank of a module " . R. Farkas -- Noetherian group rings: An exercise in creating folklore and intuition " . C. Jantzen -- Primitive ideals in the enveloping algebra of a semisimple Lie algebra " . J. Enright -- Representation theory of semisimple Lie algebras " .-E. Björk -- Filtered Noetherian rings " . Rentschler -- Primitive ideals in enveloping algebras.
Author: Bruno J. Müller
Publisher:
Published: 1977
Total Pages: 68
ISBN-13:
DOWNLOAD EBOOKAuthor: Marco Fontana
Publisher: Springer
Published: 2017-11-11
Total Pages: 374
ISBN-13: 3319658743
DOWNLOAD EBOOKThis volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non-Noetherian ring theory, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra. Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016: “Recent Advances in Commutative Ring and Module Theory,” Bressanone, Italy; “Conference on Rings and Polynomials” Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.