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IDENTITIES IN THE ALGEBRA OF PARTIAL MAPS

MARCEL JACKSON

Department of Mathematics, La Trobe University, Victoria 3086, Australia

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and

TIM STOKES

Mathematics, University of Waikato, Hamilton, New Zealand

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https://doi.org/10.1142/S0218196706003426Cited by:9 (Source: Crossref)

Abstract

We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable.

Keywords:

AMSC: 08A02, 06F05, 20M20

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