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On Some Finitary Conditions Arising from the Axiomatisability of Certain Classes of Monoid Acts
Authors:Victoria Gould  Miklós Hartmann  Lubna Shaheen
Institution:1. Department of Mathematics , University of York , Heslington , York , UK victoria.gould@york.ac.uk;3. Department of Mathematics , University of York , Heslington , York , UK;4. Mathematical Institute , University of Oxford , 24-29 St. Giles’ , Oxford , UK
Abstract: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).
Keywords:Axiomatisable class  Finitary conditions  Inverse monoid  S-act
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