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Polynomial Identities of Bernstein Algebras of Small Dimension

✍ Scribed by J Bernad; S González; C Martı́nez; A.V Iltyakov

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
237 KB
Volume
207
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

This means that any identity f of A is a consequence of identities in S, i.e., f can be obtained consequently from S by means of replacing of variables with polynomials, multiplication by polynomials and linear combination. A minimal set of generators is called a base of identities of A.

Let B be a commutative algebra and let be a nontrivial homomor-Ž . phism from B to the ground field F. Then the pair B, is called a baric Ž w x. Ž . algebra see 9 . If the baric algebra satisfies the baric identity

it is said to be a Bernstein algebra. Polynomial identities as additional finiteness conditions are useful in various subclasses of baric algebras, in Ž w x. particular, in Bernstein algebras see 2, 3, 1 .

In this paper we will describe polynomial identities of a Bernstein Ž . Ž . algebra B, of dimension F 3 in terms of generators of T B over a field of characteristic zero. Ž w x.

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