On the subsemigroup generated by ordered idempotents of a regular semigroup

• Autorzy: Anjan Kumar Bhuniya , Kalyan Hansda
• Języki publikacji: EN

Abstrakty

EN

An element $e$ of an ordered semigroup S is called an ordered idempotent if e ≤ e². Here we characterize the subsemigroup $<E_{≤}(S)>$ generated by the set of all ordered idempotents of a regular ordered semigroup S. If S is a regular ordered semigroup then $<E_{≤}(S)>$ 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.

Słowa kluczowe

EN

ordered regular; ordered inverse; ordered idempotent; downward closed; completely regular

Kategorie tematyczne

• 20M10: General structure theory
• 06F05: Ordered semigroups and monoids

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2015
• Tom: 35
• Numer: 2
• Strony: 205-211

Daty

wydano

2015

otrzymano

2015-06-16

Twórcy

autor

Anjan Kumar Bhuniya

• Department of Mathematics, Visva-Bharati, Santiniketan - 731235, India

autor

Kalyan Hansda

• Department of Mathematics, Visva-Bharati, Santiniketan - 731235, India

Bibliografia

• [1] A.K. Bhuniya and K. Hansda, Complete semilattice of ordered semigroups, communicated.
• [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
• [3] T.E. Hall, On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. 1 (1969), 195-208. doi: 10.1017/S0004972700045950
• [4] T.E. Hall, Orthodox semigroups, Pacific J. Math. 1, 677-686. doi: 10.2140/pjm.1971.39.677
• [5] T.E. Hall, On regular semigroups, J. Algebra 24 (1973), l-24. doi: 10.1016/0021-8693(73)90150-6
• [6] K. Hansda, Bi-ideals in Clifford ordered semigroup, Discuss. Math. Gen. Alg. and Appl. 33 (2013), 73-84. doi: 10.7151/dmgaa.1195
• [7] K. Hansda, Regularity of subsemigroups generated by ordered idempotents, Quasigroups and Related Systems 22 (2014), 217-222.
• [8] N. Kehayopulu, On completely regular poe-semigroups, Math. Japonica 37 (1) (1992), 123-130.
• [9] D.B. McAlister, A note on congruneces on orthodox semigroups, Glasgow J. Math. 26 (1985), 25-30. doi: 10.1017/S0017089500005735
• [10] J.C. Meakin, Congruences on orthodox semigroups, J. Austral. Math. Soc. XII (3) (1971), 222-341. doi: 10.1017/S1446788700009794
• [11] J.C. Meakin, Congruences on orthodox semigroups II, J. Austral. Math. Soc. XIII (3) (1972), 259-266. doi: 10.1017/S1446788700013665
• [12] J.E. Milles, Certain congruences on orthodox semigroups, Pacific J. Math. 64 (1) (1976), 217-226. doi: 10.2140/pjm.1976.64.217
• [13] M. Yamada, Orthodox semigroups whose idempotents satisfy a certain identity, Semigroup Forum 6 (1973), 113-128. doi: 10.1007/BF02389116

Identyfikatory

DOI

10.7151/dmgaa.1235