Rings of Infinite Matrices and Polynomial Rings PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Rings of Infinite Matrices and Polynomial Rings PDF full book. Access full book title Rings of Infinite Matrices and Polynomial Rings by Richard E. Johnson. Download full books in PDF and EPUB format.
Author: Richard E. Johnson
Publisher:
ISBN:
Category : Infinite matrices
Languages : en
Pages : 142
Get Book Here
Book Description
Author: Richard E. Johnson
Publisher:
ISBN:
Category : Infinite matrices
Languages : en
Pages : 142
Get Book Here
Book Description
Author: Eli Aljadeff
Publisher: American Mathematical Soc.
ISBN: 1470451743
Category : Education
Languages : en
Pages : 630
Get Book Here
Book Description
A 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:
ISBN:
Category : Mathematics
Languages : en
Pages : 232
Get Book Here
Book Description
Author: Vesselin Drensky
Publisher: Birkhäuser
ISBN: 3034879342
Category : Mathematics
Languages : en
Pages : 197
Get Book Here
Book Description
These 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: Vesselin Drensky
Publisher: CRC Press
ISBN: 9780824701833
Category : Mathematics
Languages : en
Pages : 332
Get Book Here
Book Description
"Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."
Author: Paul Moritz Cohn
Publisher:
ISBN:
Category : Associative rings
Languages : en
Pages : 632
Get Book Here
Book Description
Author: Michiel Hazewinkel
Publisher: CRC Press
ISBN: 1482245051
Category : Mathematics
Languages : en
Pages : 384
Get Book Here
Book Description
The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth centu
Author: Donald S. Passman
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 176
Get Book Here
Book Description
The algebraic study of group rings was initiated in 1949 by I. Kaplansky. The subject has been pursued by a small but growing number of researchers, and has reached a point in its development where a coherent account of the basic results is needed. That is the goal of this text. The topics covered are selective, with material balanced between ring theory and group theory, and a basic one year course in algebra should provide sufficient background for readers.
Author:
Publisher: Academic Press
ISBN: 0080874002
Category : Mathematics
Languages : en
Pages : 387
Get Book Here
Book Description
Polynomial Identities in Ring Theory
Author: Andrei V. Kelarev
Publisher: World Scientific
ISBN: 9810247451
Category : Mathematics
Languages : en
Pages : 218
Get Book Here
Book Description
This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs.
