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:	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
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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