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- Title
Quasiresiduals in Semigroups with Natural Partial Order.
- Authors
Mitsch, Heinz
- Abstract
A semigroup ( S, ·) is called right (left) quasiresiduated if for any a, b in S there exists x in S such that ax ≤ S b ( xa ≤ S b) with respect to the natural partial order ≤ S of S. This concept has its origin in the theory of residuated semigroups, but can also be seen as a generalization of the right (left) simplicity of semigroups. It is first studied for totally-, resp., trivially-ordered semigroups, and then for semigroups with idempotents. In particular, the cases when ( S, ≤ S) is directed downwards and when S contains a zero (with respect to a more restrictive definition) are dealt with. Throughout, examples are given; in total, 30 classes of (often well-known) semigroups of this kind are specified.
- Subjects
SEMIGROUPS (Algebra); PARTIAL algebras; GROUP theory; SEMIGROUP algebras; UNIVERSAL algebra
- Publication
Algebra Colloquium, 2017, Vol 24, Issue 3, p361
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386717000220