Journal article
Varieties of equality structures
International Journal of Algebra and Computation, Vol.13(04), pp.463-480
2003
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).
Details
- Title
- Varieties of equality structures
- Authors/Creators
- D. Fearnley-Sander (Author/Creator) - University of TasmaniaT. Stokes (Author/Creator) - Murdoch University
- Publication Details
- International Journal of Algebra and Computation, Vol.13(04), pp.463-480
- Publisher
- World Scientific Publishing
- Identifiers
- 991005541098307891
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
Metrics
41 Record Views
InCites Highlights
These are selected metrics from InCites Benchmarking & Analytics tool, related to this output
- Collaboration types
- Domestic collaboration
- Citation topics
- 9 Mathematics
- 9.280 Algebra & Topology
- 9.280.1047 Algebraic Logic
- Web Of Science research areas
- Mathematics
- ESI research areas
- Mathematics