On hopfian cofinite subsemigroups
Group Theory
2013-07-29 v1
Abstract
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 S is not finitely generated. There exists a finitely generated hopfian semigroup S with a non-hopfian subsemigroup T such that S\T has size 1.
Cite
@article{arxiv.1307.6929,
title = {On hopfian cofinite subsemigroups},
author = {Victor Maltcev and N. Ruskuc},
journal= {arXiv preprint arXiv:1307.6929},
year = {2013}
}