eCite Digital Repository
Varieties of Equality Structures
Citation
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
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 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 |
Downloads: | 0 |
Repository Staff Only: item control page