  In 1988, 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 with
nonzero T-ideal of identities that is properly contained CP(A). V. V.
Shchigolev (2001) showed that for any field k of characteristic zero, every
T-space of the infinite dimensional free associative k algebra is finitely
based, and it follows from this that every T-space of the infinite dimensional
free unitary k algebra 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 is a prime greater than 2 and k is
an arbitrary field of characteristic p, then the T-space of central polynomials
of the infinite dimension free (unitary or otherwise) associative algebra is
finitely based, thus providing a negative answer to Okhitin's question.
