num_pages: 200
description: 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.
language: English
title: Polynomial Identity Rings
publisher: Birkhauser