10 citations · 36 across the 21 of their papers we have counts for
23 papers
Two applications of monoid actions to cross-sections
Tara Brough, Alan J. Cain, Victor Maltcev
Using a construction that builds a monoid from a monoid action, this paper exhibits an example of a direct product of monoids that admits a prefix-closed regular cross-section, but…
For a few elements more: A survey of finite Rees index
Alan J. Cain, Victor Maltcev
This paper makes a comprehensive survey of results relating to finite Rees index for semigroups. In particular, we survey of the state of knowledge on whether various finiteness pr…
On hopfian cofinite subsemigroups
Victor Maltcev, N. Ruskuc
If a finitely generated semigroup S has a hopfian (meaning: every surjective endomorphism is an automorphism) cofinite subsemigroup T then S is hopfian too. This no longer holds if…
A simple non-bisimple congruence-free finitely presented monoid
Alan J. Cain, Victor Maltcev
We exhibit an example of a finitely presented monoid that is congruence-free and simple but not bisimple.
Hopfian and co-hopfian subsemigroups and extensions
Alan J. Cain, Victor Maltcev
This paper investigates the preservation of hopficity and co-hopficity on passing to finite-index subsemigroups and extensions. It was already known that hopficity is not preserved…
A countable family of finitely presented infinite congruence-free monoids
Alan J. Cain, Victor Maltcev, Abdullahi Umar
We prove that monoids are congruence-free for all . This provides a ne…