Polynomial Identity Rings

Vesselin Drensky, Edward Formanek - Collection Advanced Courses in Mathematics - CRM Barcelona

200 pages, parution le 01/10/2004

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Résumé

A ring R satisfies a polynomial identity if there is a polynomial f in noncommuting variables which vanishes under substitutions from R. For example, commutative rings satisfy the polynomial f(x,y) = xy - yx and exterior algebras satisfy the polynomial f(x,y,z) = (xy - yx)z - z(xy - yx). "Satisfying a polynomial identity" is often regarded as a generalization of commutativity. These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The former studies the ideal of polynomial identities satisfied by a ring R. The latter studies the properties of rings which satisfy a polynomial identity. 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. The intended audience is graduate students in algebra, and researchers in algebra, combinatorics and invariant theory.

Written for:
Graduates, postgraduates and researchers in Combinatorics and Algebra; Computer Science, Cryptology

Sommaire

Foreword
Part A. Combinatorial Aspects in PI-Rings (by V. Drensky)
Part B. Polynomial Identity Rings (by E. Formanek)
Bibliography
Index.

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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Vesselin Drensky, Edward Formanek
Collection	Advanced Courses in Mathematics - CRM Barcelona
Parution	01/10/2004
Nb. de pages	200
Format	17 x 24
Couverture	Broché
Poids	510g
Intérieur	Noir et Blanc
EAN13	9783764371265