Author : M. Parvathi Banu 1
Date of Publication :13th April 2018
Abstract: In this paper, left singularity and left regularity in a near-idempotent – semigroup are defined. In a nearidempotent – semigroup a is left singular and it is also proved that every class in a near-idempotent – semigroup is left (right) singular if and only if S is left (right) regular. - class is defined and proved that it is a near null semigroup. Also a b for all a,b in S and ab= a in a left singular near-idempotent – semigroup. Any nearidempotent – semigroup is left regular if and only if = and right regular if = . Also any near idempotent – semigroup is near-commutative if = . Any near-commutative – semigroup is near commutative if only and only if it is both left and right regular.
Reference :
-
- Clifford, A.H. and Preston, G.B., “ The Algebraic Theory of Semigroups”, Vol. I,Providence, 1961
- A. H. Clifford, Bands of semigroups, Proc. Amer. Math. Soc. 5 (1954), 499-504
- Jayalakshmi, A., “ Some Studies in Algebraic Semigroups and Associated Structures”, Doctoral Thesis, Bangalore University, 1981.
- T.N. Kavitha, A.Jayalakshmi, On near – idempotent semigroups, Vol 5, No 5, International Journal of Mathematical Archive May 2014.
- T.N. Kavitha, A. Jayalakshmi, Rectangular nearidempotent semigroup, -selected for presentation and publication at the international conference on mathematical science- 2014 and will be published in mathematical science international research journal, Vol 3, issue 2.
- T.N. Kavitha, A. Jayalakshmi, Some Special Types Of Near idempotent Semigroup – selected for presentation and publication at the IMRF international conference – 2014, Thailand and will be published in
- 7. Kimura, N., The Structure of Idempotent Semigroups ( I ), Pacific J. of Math.(1958)
- Naoki Kimura, Note on idempotent semigroups. II, Proc. Japan. Acad. 34 (1958), 110-112
- Naoki Kimura, On semigroups, Dissertation, Tulane University (1957), 1-133. 10. Mc Lean, D., Idempotent Semigroup, Am. Math. Mon. 61 (1954)
- Yamada. M, on the greatest semilattice decomposition of a semigroup, Kodai math. Sem. Rep.7 (1955) (59-62 Mathematical Science International Research Journal- Vol 3, special issue.
- Jayalakshmi, A., and. Atre. Ananth K. “ On Generalization of the concept of Inflation of semigroups” Academic Journal of Sciences”, CD. ROM. ISSN 2165 – 6282:: 2(2): 527- 532(2013).