Examples of associative algebras for which the <Emphasis Type="Italic">T</Emphasis>-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(M ₂(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 k ₀〈X〉 is finitely based, and it follows from this that every T-space of k ₁〈X〉 is also finitely based. This more than answers Okhitin’s question (in the affirmative) for fields of characteristic zero.