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Varieties of Equality Structures
journal contribution
posted on 2023-05-16, 14:14 authored by Fearnley-Sander, DP, Stokes, TWe 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).
History
Publication title
International Journal of Algebra and ComputationVolume
13Issue
4Pagination
463-480ISSN
0218-1967Department/School
School of Natural SciencesPublisher
World Scientific Publ Co Pte LtdPlace of publication
SingaporeRepository Status
- Restricted