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Varieties of Equality Structures


Fearnley-Sander, DP and Stokes, T, Varieties of Equality Structures, International Journal of Algebra and Computation, 13, (4) pp. 463-480. ISSN 0218-1967 (2003) [Refereed Article]

DOI: doi:10.1142/S021819670300147X


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 Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Algebra and number theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Fearnley-Sander, DP (Mr Desmond Fearnley-Sander)
ID Code:27029
Year Published:2003
Web of Science® Times Cited:7
Deposited By:Mathematics
Deposited On:2003-08-01
Last Modified:2004-04-20

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