Jackson, M. & Stokes, T. E.(2006) Identities in the algebra of partial maps. International Journal of Algebra and Computation, 16(6), 1131-1159.
Permanent Research Commons link: http://hdl.handle.net/10289/2007
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.
World Scientific Publishing
This is an author’s version of an article published in the journal: International Journal of Algebra and Computation. ©2006 World Scientific Publishing Company, http://www.worldscinet.com/ijac/ijac.shtml