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On diagonal acts of monoids

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Abstract

It is proved that the monoid R-N of all partial recursive functions of one variable is finitely generated, and that R-N x R-N is a cyclic (left and right) R-N-act (under the natural diagonal actions s(alpha, b) = (s alpha, sb), (alpha, b)s = (alphas, bs)). We also construct a finitely presented monoid S such that S x S is a cyclic left and right S-act, and study further interesting properties of diagonal acts and their relationship with power monoids.

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Original languageEnglish
Pages (from-to)167-175
Number of pages9
JournalBulletin of the Australian Mathematical Society
Volume63
Issue number1
DOIs
Publication statusPublished - Feb 2001

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