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Computational Aspects of Polynomial Identities - Volume l, Kemer's Theorems, 2nd Edition (Hardcover, 2nd edition)
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Computational Aspects of Polynomial Identities - Volume l, Kemer's Theorems, 2nd Edition (Hardcover, 2nd edition)
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Total price: R5,377
Discovery Miles: 53 770
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Computational Aspects of Polynomial Identities: Volume l, Kemer's
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 Kemer's proof of Specht's conjecture for affine
PI-algebras in characteristic 0. The book first discusses the
theory needed for Kemer's 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
Specht's conjecture in characteristic p as well as the underlying
theory. The book also covers Noetherian PI-algebras,
Poincare-Hilbert series, Gelfand-Kirillov 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 Rosset's proof
of the Amitsur-Levitzki 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.
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