Varieties of equality structures
Fearnley-Sander, D. and Stokes, T. (2003) Varieties of equality structures. International Journal of Algebra and Computation, 13 (04). pp. 463-480.
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Abstract
We consider universal algebras which are monoids and which have a binary operation we call internalized equality, satisfying some natural conditions. We show that the class of such E-structures has a characterization in terms of a distinguished submonoid which is a semilattice. Some important varieties (and variety-like classes) of E-structures are considered, including E-semilattices (which we represent in terms of topological spaces), E-rings (which we show are equivalent to rings with a generalized interior operation), E-quantales (where internalized equalities on a fixed quantale in which 1 is the largest element are shown to correspond to sublocales of the quantale), and EI-structures (in which an internalized inequality is defined and interacts in a natural way with the equality operation).
Item Type: | Journal Article |
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Murdoch Affiliation(s): | School of Mathematical and Physical Sciences |
Publisher: | World Scientific Publishing |
URI: | http://researchrepository.murdoch.edu.au/id/eprint/33692 |
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