Turkish Journal of Mathematics
Author ORCID Identifier
NAREUPANAT LEKKOKSUNG: 0000-0002-0026-8387
Abstract
The concept of simplicity in le-semigroups has been used to characterize the coincidence of ideal elements and to study Khayopulu–Green’s relations. Several types of simplicities are known, including two-sided simplicity, left simplicity, right simplicity, bisimplicity, quasisimplicity, and biinterior simplicity. A natural question arises: are there further notions of simplicity for le-semigroups? If so, how are they related? By employing the notion of partition ideal elements, we observe that several potential simplicities have not yet been explored. In this paper, we introduce new forms of simplicity in le-semigroups defined via partitions of full words, and we investigate the connections among these simplicities. Finally, we apply these notions of simplicity to determine the regularities and ideal elements of le-semigroups.
DOI
10.55730/1300-0098.3646
Keywords
ordered semigroup, $le$-semigroup, ideal element, simplicity
First Page
208
Last Page
227
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
LEKKOKSUNG, N (2026). Simplicity in le-semigroups via partitions of full words, and its applications to regularity conditions induced by linear inequalities. Turkish Journal of Mathematics 50 (2): 208-227. https://doi.org/10.55730/1300-0098.3646
