Two applications of monoid actions to cross-sections

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Using a construction that builds a monoid from a monoid action, this article exhibits an example of a direct product of monoids that admits a prefix-closed regular cross-section, but one of whose factors does not admit a regular cross-section; this answers negatively an open question from the theory of Markov monoids. The same construction is then used to show that for any full trios C and D such that C is not a subclass of D there is a monoid with a cross-section in C but no cross-section in D.

Original languageEnglish
JournalCommunications in Algebra
Publication statusAccepted/In press - 13 Nov 2019

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