On some finitary conditions arising from the axiomatisability of certain classes of monoid acts

Victoria Gould, Miklos Hartmann, Lubna Shaheen

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This article considers those monoids S satisfying one or both of the finitary properties (R) and (r), focussing for the most part on inverse monoids. These properties arise from questions of axiomatisability of classes of S-acts, and appear to be of interest in their own right. If S is weakly right noetherian (WRN), that is, S has the ascending chain condition on right ideals, then certainly (r) holds. Other than this, we show that (R), (r) and (WRN) are independent. Our most detailed results are for Clifford monoids, in which case we completely characterise those S with trivial structure homomorphisms satisfying (R) or (r).
Original languageEnglish
Pages (from-to)2584-2602
Number of pages19
JournalCommunications in Algebra
Issue number6
Early online date1 Feb 2014
Publication statusPublished - Jun 2014


  • inverse monoid
  • S-act
  • axiomatisable class

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