Alan J. Cain

most citedA countable family of finitely presented infinite congruence-free monoids

2 citations · 3 across the 3 of their papers we have counts for

collaborators

3 papers

math.GR2013★ 2 cited

A countable family of finitely presented infinite congruence-free monoids

Alan J. Cain, Victor Maltcev, Abdullahi Umar

We prove that monoids $Mon ⟨ a, b, c, d : a^{n} b = 0, a c = 1, d b = 1, d c = 1, d ab = 1, d a^{2} b = 1, \dots, d a^{n - 1} b = 1 ⟩$ are congruence-free for all $n \geq 1$ . This provides a ne…

math.CO2013★ 1 cited

Unary FA-presentable binary relations: transitivity and classification results

Alan J. Cain, Nik Ruškuc

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision…

math.GR2013

Monoids $Mon ⟨ a, b : a^{α} b^{β} a^{γ} b^{δ} = b ⟩$ admit finite complete rewriting systems

Alan Cain, Victor Maltcev

We prove that every monoid $Mon ⟨ a, b : a^{α} b^{β} a^{γ} b^{δ} = b ⟩$ admits a finite complete rewriting system. Furthermore we prove that $\mathrm{Mon}\langle a,b:ab^2a^2b^2=…

A countable family of finitely presented infinite congruence-free monoids

Unary FA-presentable binary relations: transitivity and classification results

Monoids Mon⟨a,b:aαbβaγbδ=b⟩ admit finite complete rewriting systems

Monoids $Mon ⟨ a, b : a^{α} b^{β} a^{γ} b^{δ} = b ⟩$ admit finite complete rewriting systems