Turkish Journal of Mathematics
Author ORCID Identifier
MICHAEL TSINGELIS: 0000-0002-4929-3006
Abstract
A partial one-to-one mapping on a set X is a mapping whose domain is a subset of X. The set of partial one-one mappings on a set X is an inverse semigroup (the symmetric inverse semigroup on X). An element x of an ordered semigroup (S, ·, ≤) is called an inverse element of α ∈ S if α ≤ xαx and x ≤ xαx. An inverse ordered semigroup is an ordered semigroup S for which every element of S possesses an inverse element and the inverse elements of any element of S are in the same connected component of the Hasse diagram of its order relation. In the paper, we give an analogous result to the Vagner-Preston Representation for inverse ordered semigroups by proving that for every inverse ordered semigroup S there exists an ℛ≤-monoantimorphism from S to the symmetric inverse semigroup on S.
DOI
10.55730/1300-0098.3637
Keywords
Inverse ordered semigroup, relation ℛ≤, symmetric inverse semigroup on a set X, Vagner-Preston Representation, ℛ≤-monoantimorphism
First Page
87
Last Page
96
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
TSINGELIS, M (2026). Representation of inverse ordered semigroups by means of symmetric inverse semigroups on a set. Turkish Journal of Mathematics 50 (1): 87-96. https://doi.org/10.55730/1300-0098.3637
