Research Article
BibTex RIS Cite

ON RIGHT INVERSE $\Gamma$-SEMIGROUP

Year 2015, Volume: 3 Issue: 2, 140 - 151, 01.10.2015

Abstract

Let S = fa; b; c; : : : g and 􀀀 = f ; ; ; : : : g be two nonempty sets. S is called a 􀀀-semigroup if a b 2 S, for all 2 􀀀 and a; b 2 S and (a b) c = a (b c), for all a; b; c 2 S and for all ; 2 􀀀. An element e 2 S is said to be -idempotent for some 2 􀀀 if e e = e. A 􀀀- semigroup S is called regular 􀀀-semigroup if each element of S is regular i.e, for each a 2 S there exists an element x 2 S and there exist ; 2 􀀀 such that a = a x a. A regular 􀀀-semigroup S is called a right inverse 􀀀-semigroup if for any - idempotent e and -idempotent f of S, e f e = f e. In this paper we introduce ip - congruence on regular 􀀀-semigroup and ip - congruence pair on right inverse 􀀀-semigroup and investigate some results relating this pair.

References

  • [1] F. Pastijn and M. Petrich., Congruences on regular semigroups, Trans. Amer. Math. Soc., 295(1986), 607-633.
  • [2] G.M.S. Gomes., R-unipotent congruences on regular semigroups, emigroup Forum, 31(1985), 265-280.
  • [3] J.M. Howie, An introduction to semigroup Theory, Clarendon Press, Oxford, 1995,
  • [4] K.S.S. Nambooripad, Structure of regular semigroups I, Mem. Amer. Math. Soc. 22 (1979), no.224.
  • [5] M.K. Sen, M.K. and N.K. Saha., On 􀀀-semigroup I , Bull. Cal. Math. Soc., 78(1986), 180-186.
  • [6] N.K. Saha., On 􀀀-semigroup II, Bull. Cal. Math. Soc, 79(1987), 331-335.
  • [7] N.K. Saha., On 􀀀-semigroup III, Bull. Cal. Math. Soc., 80(1988), 1-12.
  • [8] S. Chattopadhyay., Right inverse 􀀀-semigroup, Bull. Cal. Math. Soc., 93(6),(2001), 435-442.
  • [9] S. Chattopadhyay., Right orthodox 􀀀-semigroup, Southeast Asian Bull. of Mathemat- ics,(2005)29, 1-18.
  • [10] S. Chattopadhyay., Sandwich sets on regular 􀀀-semigroup, Communicated.
Year 2015, Volume: 3 Issue: 2, 140 - 151, 01.10.2015

Abstract

References

  • [1] F. Pastijn and M. Petrich., Congruences on regular semigroups, Trans. Amer. Math. Soc., 295(1986), 607-633.
  • [2] G.M.S. Gomes., R-unipotent congruences on regular semigroups, emigroup Forum, 31(1985), 265-280.
  • [3] J.M. Howie, An introduction to semigroup Theory, Clarendon Press, Oxford, 1995,
  • [4] K.S.S. Nambooripad, Structure of regular semigroups I, Mem. Amer. Math. Soc. 22 (1979), no.224.
  • [5] M.K. Sen, M.K. and N.K. Saha., On 􀀀-semigroup I , Bull. Cal. Math. Soc., 78(1986), 180-186.
  • [6] N.K. Saha., On 􀀀-semigroup II, Bull. Cal. Math. Soc, 79(1987), 331-335.
  • [7] N.K. Saha., On 􀀀-semigroup III, Bull. Cal. Math. Soc., 80(1988), 1-12.
  • [8] S. Chattopadhyay., Right inverse 􀀀-semigroup, Bull. Cal. Math. Soc., 93(6),(2001), 435-442.
  • [9] S. Chattopadhyay., Right orthodox 􀀀-semigroup, Southeast Asian Bull. of Mathemat- ics,(2005)29, 1-18.
  • [10] S. Chattopadhyay., Sandwich sets on regular 􀀀-semigroup, Communicated.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Sumanta Chattopadhyay This is me

Publication Date October 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Chattopadhyay, S. (2015). ON RIGHT INVERSE $\Gamma$-SEMIGROUP. Konuralp Journal of Mathematics, 3(2), 140-151.
AMA Chattopadhyay S. ON RIGHT INVERSE $\Gamma$-SEMIGROUP. Konuralp J. Math. October 2015;3(2):140-151.
Chicago Chattopadhyay, Sumanta. “ON RIGHT INVERSE $\Gamma$-SEMIGROUP”. Konuralp Journal of Mathematics 3, no. 2 (October 2015): 140-51.
EndNote Chattopadhyay S (October 1, 2015) ON RIGHT INVERSE $\Gamma$-SEMIGROUP. Konuralp Journal of Mathematics 3 2 140–151.
IEEE S. Chattopadhyay, “ON RIGHT INVERSE $\Gamma$-SEMIGROUP”, Konuralp J. Math., vol. 3, no. 2, pp. 140–151, 2015.
ISNAD Chattopadhyay, Sumanta. “ON RIGHT INVERSE $\Gamma$-SEMIGROUP”. Konuralp Journal of Mathematics 3/2 (October 2015), 140-151.
JAMA Chattopadhyay S. ON RIGHT INVERSE $\Gamma$-SEMIGROUP. Konuralp J. Math. 2015;3:140–151.
MLA Chattopadhyay, Sumanta. “ON RIGHT INVERSE $\Gamma$-SEMIGROUP”. Konuralp Journal of Mathematics, vol. 3, no. 2, 2015, pp. 140-51.
Vancouver Chattopadhyay S. ON RIGHT INVERSE $\Gamma$-SEMIGROUP. Konuralp J. Math. 2015;3(2):140-51.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.