On separability properties in direct products of semigroups
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.
Citation
O'Reilly , G A , Quick , M & Ruskuc , N 2021 , ' On separability properties in direct products of semigroups ' , Monatshefte für Mathematik , vol. 197 , no. 2 , pp. 333-352 . https://doi.org/10.1007/s00605-021-01570-4
Publication
Monatshefte für Mathematik
Status
Peer reviewed
ISSN
0026-9255Type
Journal article
Collections
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