11 citations · 15 across the 10 of their papers we have counts for
14 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…
O-cycles, vertex-oriented graphs, and the four colour theore
Ortho Flint, Stuart Rankin
In 1880, P. G. Tait showed that the four colour theorem is equivalent to the assertion that every 3-regular planar graph without cut-edges is 3-edge-colourable, and in 1891, J. Pet…
Fine-Wilf graphs and the generalized Fine-Wilf theorem
Stuart A. Rankin
In 1962, R. C. Lyndon and M. P. Shutzenberger established that for any positive integers r and s, any sequence of length at least r+s that is both r-periodic and s-periodic is then…