Polynomial Identity Rings (Advanced Courses in Mathematics - CRM Barcelona)
Edition: 1 edition
Publisher: Birkhäuser Basel
Published: July 12, 2004
Language: eng
Format: Paperback
Number of pages: 200
ISBN-13: 9783764371265
Subjects: Algebraic number theory; Invariants; Computers - General Information; Mathematics; Science/Mathematics; Polynomial rings; Algebra - General; Computer Science; Discrete Mathematics; Combinatorics; Commutative Algebras; Finite Dimensional Algebras; Mathematics / Algebra / General; Polynomial Identity Algebras; Polynomial Identity Rings; General; Matrices
First sentence: Throughout this part devoted to the combinatorial aspects in Pi-rings we fix a field A'.
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.