Examples of associative algebras for which the T-space of central polynomials is not finitely based
In 1988 (see [7]), S. V. Okhitin proved that for any field k of characteristic zero, the T-space CP(M2(k)) is finitely based, and he raised the question as to whether CP(A) is finitely based for every (unitary) associative algebra A for which 0 ≠ T(A) ⊊ CP(A). V. V. Shchigolev (see [9], 2001) showed that for any field of characteristic zero, every T-space of k0〈X〉 is finitely based, and it follows from this that every T-space of k1〈X〉 is also finitely based. This more than answers Okhitin’s question (in the affirmative) for fields of characteristic zero.For a field of characteristic 2, the infinite-dimensional Grassmann algebras, unitary and nonunitary, are commutative and thus the T-space of central polynomials of each is finitely based.We shall show in the following that if p > 2 and k is an arbitrary field of characteristic p, then neither CP(G0) nor CP(G) is finitely based, thus providing a negative answer to Okhitin’s question.
Examples of T-spaces with an?infinite basis
This work is devoted to the construction of T-spaces with an infinite basis over a field of finite characteristic and over some other rings. Examples of T-spaces are given that are generated by polynomials in two variables or by polynomials of bounded degree in each variable.
Ideals of Identities of Associative Algebras
Concerns the study of the structure of identities of PI-algebras over a field of characteristic zero. The author brings out the connection between varieties of algebras and finitely-generated PI-superalgebras and the book closes with an application of methods and results established earlier.