Computational Aspects of Polynomial Identities

Computational Aspects of Polynomial Identities: Volume l, Kemers Theorems, 2nd Edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. This edition gives all the details involved in Kemers proof of Spechts conjecture for affine PI-algebras in characteristic 0. The book first discusses the theory needed for Kemers proof, including the featured role of Grassmann algebra and the translation to superalgebras. The authors develop Kemer polynomials for arbitrary varieties as tools for proving diverse theorems. They also lay the groundwork for analogous theorems that have recently been proved for Lie algebras and alternative algebras. They then describe counterexamples to Spechts conjecture in characteristic p as well as the underlying theory. The book also covers Noetherian PI-algebras, PoincarHilbert series, GelfandKirillov dimension, the combinatoric theory of affine PI-algebras, and homogeneous identities in terms of the representation theory of the general linear group GL. Through the theory of Kemer polynomials, this edition shows that the techniques of finite dimensional algebras are available for all affine PI-algebras. It also emphasizes the Grassmann algebra as a recurring theme, including in Rossets proof of the AmitsurLevitzki theorem, a simple example of a finitely based T-ideal, the link between algebras and superalgebras, and a test algebra for counterexamples in characteristic p.