On separability properties in direct products of semigroups
| Autor: | Nik Ruskuc, Gerard O'Reilly, Martyn Quick |
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| Přispěvatelé: | University of St Andrews. Pure Mathematics, University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Property (philosophy) General Mathematics T-NDAS Separability Subsemigroup separability Mathematics::General Topology 0102 computer and information sciences Group Theory (math.GR) Residual Congruences 01 natural sciences Mathematics::Group Theory Residual properties FOS: Mathematics QA Mathematics Finite index congruence 0101 mathematics QA Direct product Mathematics Direct products Residual finiteness 010102 general mathematics Mathematics::Rings and Algebras Mathematics - Rings and Algebras Congruence relation Complete separability 20M10 (Primary) 20E26 08A30 (Secondary) 010201 computation theory & mathematics Rings and Algebras (math.RA) Semigroups Mathematics - Group Theory |
| DOI: | 10.48550/arxiv.2102.10872 |
| Popis: | 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. Comment: Revised version. To appear Monatsh. Math |
| Databáze: | OpenAIRE |
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