11 citations · 14 across the 6 of their papers we have counts for
9 papers
Maximal T-spaces of the free associative algebra over a finite field
Chuluun Bekh-Ochir, Stuart Rankin
In earlier work, it was established that for any finite field k, the free associative k-algebra on one generator x, denoted by k[x]_0, had infinitely many maximal T-spaces, but exa…
Maximal T-spaces of a free associative algebra
Chuluun Bekh-Ochir, Stuart Rankin
We study the lattice of T-spaces of a free associative k-algebra over a nonempty set. It is shown that when the field k is infinite, then the lattice has a maximum element, and tha…
On a conjecture of V. V. Shchigolev
C. Bekh-Ochir, S. A. Rankin
V. V. Shchigolev has proven that over any infinite field k of characteristic p>2, the T-space generated by G={x_1^p,x_1^px_2^p,...} is finitely based, which answered a question rai…
On a problem of A. V. Grishin
C. Bekh-Ochir, S. A. Rankin
In this note, we offer a short proof of V. V. Shchigolev's result that over any field k of characteristic p>2, the T-space generated by x_1^p,x_1^px_2^p,... is finitely based, whic…
The identities and the central polynomials of the infinite dimensional unitary Grassmann algebra over a finite field
C. Bekh-Ochir, S. A. Rankin
We describe the T-ideal of identities and the T-space of central polynomials for the infinite dimensional unitary Grassmann algebra over a finite field.
Examples of associative algebras for which the T-space of central polynomials is not finitely based
C. Bekh-Ochir, S. A. Rankin
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 base…