Polynomial Identity Rings

Vesselin Drensky

ISBN 10: 3764371269 / ISBN 13: 9783764371265

Published by Springer, Basel, Birkhäuser Basel, Birkhäuser Mai 2004, 2004

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 200 pp. Englisch.

Seller Inventory # 9783764371265

Bibliographic Details

• Title: Polynomial Identity Rings
• Publisher: Springer, Basel, Birkhäuser Basel, Birkhäuser Mai 2004
• Publication Date: 2004
• Language: English
• ISBN 10: 3764371269
• ISBN 13: 9783764371265
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 203H x 38D millimeters 254 millimeters width by 203 millimeters height by 38 millimeters depth
• Weight: 512 grams

About this title

Synopsis

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.

Review

From the reviews:

“The book under review consists of two excellent monographs on the PI-theory by two leading researchers, V. Drensky and E. Formanek ... In summary, both expositions are very well written, and the book is recommended both for graduate students and researchers.” (MATHEMATICAL REVIEWS)