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Separability conditions in acts over monoids - MaRDI portal

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Separability conditions in acts over monoids

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Publication:6379667

DOI10.1007/S10474-022-01244-ZarXiv2110.03419MaRDI QIDQ6379667

Author name not available (Why is that?)

Publication date: 7 October 2021

Abstract: We discuss residual finiteness and several related separability conditions for the class of monoid acts, namely weak subact separability, strong subact separability and complete separability. For each of these four separability conditions, we investigate which monoids have the property that all their (finitely generated) acts satisfy the condition. In particular, we prove that: all acts over a finite monoid are completely separable (and hence satisfy the other three separability conditions); all finitely generated acts over a finitely generated commutative monoid are residually finite and strongly subact separable (and hence weakly subact separable); all acts over a commutative idempotent monoid are residually finite and strongly subact separable; and all acts over a Clifford monoid are strongly subact separable.





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