On separability properties in direct products of semigroups
Rings and Algebras
2021-05-12 v2 Group Theory
Abstract
We investigate four finiteness conditions related to residual finiteness: complete separability, strong subsemigroup separability, weak subsemigroup separability and monogenic subsemigroup separability. For each of these properties we examine under which conditions the property is preserved under direct products. We also consider if any of the properties are inherited by the factors in a direct product. We give necessary and sufficient conditions for finite semigroups to preserve the properties of strong subsemigroup separability and monogenic subsemigroup separability in a direct product.
Cite
@article{arxiv.2102.10872,
title = {On separability properties in direct products of semigroups},
author = {Gerard O'Reilly and Martyn Quick and Nik Ruskuc},
journal= {arXiv preprint arXiv:2102.10872},
year = {2021}
}
Comments
Revised version. To appear Monatsh. Math