Overview
- 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
Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)
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Table of contents (27 chapters)
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Front Matter
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Combinatorial Aspects in PI-Rings
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Front Matter
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Polynomial Identity Rings
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Front Matter
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Keywords
About this book
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.
Reviews
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)
Authors and Affiliations
Bibliographic Information
Book Title: Polynomial Identity Rings
Authors: Vesselin Drensky, Edward Formanek
Series Title: Advanced Courses in Mathematics - CRM Barcelona
DOI: https://doi.org/10.1007/978-3-0348-7934-7
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 2004
Softcover ISBN: 978-3-7643-7126-5Published: 25 May 2004
eBook ISBN: 978-3-0348-7934-7Published: 06 December 2012
Series ISSN: 2297-0304
Series E-ISSN: 2297-0312
Edition Number: 1
Number of Pages: VII, 200