Author :
Publisher : Academic Press
Page : 387 pages
File Size : 34,27 MB
Release : 1980-07-24
Category : Mathematics
ISBN : 0080874002
Polynomial Identities in Ring Theory
Author : Vesselin Drensky
Publisher : Birkhäuser
Page : 197 pages
File Size : 37,55 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034879342
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 : Onofrio Mario Di Vincenzo
Publisher : Springer Nature
Page : 421 pages
File Size : 30,28 MB
Release : 2021-03-22
Category : Mathematics
ISBN : 3030631117
This volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. The purpose of the book is to present the current state of the art in the theory of PI-algebras. The review of the classical results in the last few years has pointed out new perspectives for the development of the theory. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems. It is addressed to researchers in the field.
Author : Eli Aljadeff
Publisher :
Page : pages
File Size : 45,47 MB
Release : 2020
Category : PI-algebras
ISBN : 9781470456955
Author : A. Giambruno
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 27,71 MB
Release : 2005
Category : Mathematics
ISBN : 0821838296
This book gives a state of the art approach to the study of polynomial identities satisfied by a given algebra by combining methods of ring theory, combinatorics, and representation theory of groups with analysis. The idea of applying analytical methods to the theory of polynomial identities appeared in the early 1970s and this approach has become one of the most powerful tools of the theory. A PI-algebra is any algebra satisfying at least one nontrivial polynomial identity. This includes the polynomial rings in one or several variables, the Grassmann algebra, finite-dimensional algebras, and many other algebras occurring naturally in mathematics. The core of the book is the proof that the sequence of co-dimensions of any PI-algebra has integral exponential growth - the PI-exponent of the algebra. Later chapters further apply these results to subjects such as a characterization of varieties of algebras having polynomial growth and a classification of varieties that are minimal for a given exponent.
Author : Antonio Giambruno
Publisher : CRC Press
Page : 442 pages
File Size : 24,70 MB
Release : 2003-05-20
Category : Mathematics
ISBN : 9780203911549
Polynomial Identities and Combinatorial Methods presents a wide range of perspectives on topics ranging from ring theory and combinatorics to invariant theory and associative algebras. It covers recent breakthroughs and strategies impacting research on polynomial identities and identifies new concepts in algebraic combinatorics, invariant and representation theory, and Lie algebras and superalgebras for novel studies in the field. It presents intensive discussions on various methods and techniques relating the theory of polynomial identities to other branches of algebraic study and includes discussions on Hopf algebras and quantum polynomials, free algebras and Scheier varieties.
Author : Konstant I. Beidar
Publisher : CRC Press
Page : 546 pages
File Size : 20,84 MB
Release : 1995-11-17
Category : Mathematics
ISBN : 9780824793258
"Discusses the latest results concerning the area of noncommutative ring theory known as the theory of generalized identities (GIs)--detailing Kharchenko's results on GIs in prime rings, Chuang's extension to antiautomorphisms, and the use of the Beidar-Mikhalev theory of orthogonal completion in the semiprime case. Provides novel proofs of existing results."
Author : Claudio Procesi
Publisher :
Page : 232 pages
File Size : 42,11 MB
Release : 1973
Category : Mathematics
ISBN :
Author : A. Giambruno
Publisher : American Mathematical Soc.
Page : 283 pages
File Size : 22,13 MB
Release : 2009
Category : Mathematics
ISBN : 0821847716
Represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. This title contains results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras.
Author : B. Stenström
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 40,8 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642660665
The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really develop until the end of the 1950's, when a number of important papers appeared (by R. E. Johnson, Y. Utumi, A. W. Goldie, P. Gabriel, J. Lambek, and others). Since then the progress has been rapid, and the subject has by now attained a stage of maturity, where it is possible to make a systematic account of it (which is the purpose of this book). The most immediate example of a ring of quotients is the field of fractions Q of a commutative integral domain A. It may be characterized by the two properties: (i) For every qEQ there exists a non-zero SEA such that qSEA. (ii) Q is the maximal over-ring of A satisfying condition (i). The well-known construction of Q can be immediately extended to the case when A is an arbitrary commutative ring and S is a multiplicatively closed set of non-zero-divisors of A. In that case one defines the ring of fractions Q = A [S-l] as consisting of pairs (a, s) with aEA and SES, with the declaration that (a, s)=(b, t) if there exists UES such that uta = usb. The resulting ring Q satisfies (i), with the extra requirement that SES, and (ii).
