Polynomial Identity Rings
Formanek, Edward, Drensky, Vesselin
| Autor: | Drensky, Vesselin Formanek, Edward |
|---|---|
| Themengebiete: | Polynom |
| Veröffentlichungsdatum: | 25.05.2004 |
| EAN: | 9783764371265 |
| Auflage: | 2004 |
| Sprache: | Englisch |
| Seitenzahl: | 212 |
| Produktart: | Kartoniert / Broschiert |
| Verlag: | Birkhäuser Basel Springer Springer Basel AG |
Produktinformationen "Polynomial Identity Rings"
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.
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