On the subsemigroup generated by ordered idempotents of a regular semigroup

Anjan Kumar Bhuniya; Kalyan Hansda

Discussiones Mathematicae - General Algebra and Applications, Tome 35 (2015), p. 205-211 / Harvested from The Polish Digital Mathematics Library

Access to full text
Full (PDF)

Résumé

An element $e$ of an ordered semigroup S is called an ordered idempotent if e ≤ e². Here we characterize the subsemigroup $g e n e r a t e d b y t h e s e t o f a l l o r d e r e d i d e m p o t e n t s o f a r e g u l a r o r d e r e d s e m i g r o u p S . I f S i s a r e g u l a r o r d e r e d s e m i g r o u p t h e n$ is also regular. If S is a regular ordered semigroup generated by its ordered idempotents then every ideal of S is generated as a subsemigroup by ordered idempotents.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:276485

@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1235,
     author = {Anjan Kumar Bhuniya and Kalyan Hansda},
     title = {On the subsemigroup generated by ordered idempotents of a regular semigroup},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {35},
     year = {2015},
     pages = {205-211},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1235}
}

Anjan Kumar Bhuniya; Kalyan Hansda. On the subsemigroup generated by ordered idempotents of a regular semigroup. Discussiones Mathematicae - General Algebra and Applications, Tome 35 (2015) pp. 205-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1235/

Bibliographie

[000] [1] A.K. Bhuniya and K. Hansda, Complete semilattice of ordered semigroups, communicated.

[001] [2] C. Eberhart, W. Williams and I. Kinch, Idempotent-generated regular semigroups, J. Austral. Math. Soc. 15 (1) (1973), 35-41. doi: 10.1017/S1446788700012726

[002] [3] T.E. Hall, On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. 1 (1969), 195-208. doi: 10.1017/S0004972700045950 | Zbl 0172.31101

[003] [4] T.E. Hall, Orthodox semigroups, Pacific J. Math. 1, 677-686. doi: 10.2140/pjm.1971.39.677 | Zbl 0232.20124

[004] [5] T.E. Hall, On regular semigroups, J. Algebra 24 (1973), l-24. doi: 10.1016/0021-8693(73)90150-6

[005] [6] K. Hansda, Bi-ideals in Clifford ordered semigroup, Discuss. Math. Gen. Alg. and Appl. 33 (2013), 73-84. doi: 10.7151/dmgaa.1195 | Zbl 1303.06014

[006] [7] K. Hansda, Regularity of subsemigroups generated by ordered idempotents, Quasigroups and Related Systems 22 (2014), 217-222. | Zbl 1314.06017

[007] [8] N. Kehayopulu, On completely regular poe-semigroups, Math. Japonica 37 (1) (1992), 123-130. | Zbl 0745.06007

[008] [9] D.B. McAlister, A note on congruneces on orthodox semigroups, Glasgow J. Math. 26 (1985), 25-30. doi: 10.1017/S0017089500005735 | Zbl 0549.20047

[009] [10] J.C. Meakin, Congruences on orthodox semigroups, J. Austral. Math. Soc. XII (3) (1971), 222-341. doi: 10.1017/S1446788700009794 | Zbl 0234.20037

[010] [11] J.C. Meakin, Congruences on orthodox semigroups II, J. Austral. Math. Soc. XIII (3) (1972), 259-266. doi: 10.1017/S1446788700013665 | Zbl 0265.20056

[011] [12] J.E. Milles, Certain congruences on orthodox semigroups, Pacific J. Math. 64 (1) (1976), 217-226. doi: 10.2140/pjm.1976.64.217

[012] [13] M. Yamada, Orthodox semigroups whose idempotents satisfy a certain identity, Semigroup Forum 6 (1973), 113-128. doi: 10.1007/BF02389116 | Zbl 0255.20038