L(R) Cyclic Semigroups Satisfying The Identity : abc = ac

Authors

  • D. D. Padma Priya  Sr. Assistant Professor, Department of Mathematics, New Horizon College of Engineering, Bangalore, India
  • G. Shobhalatha  Professor, Department of Mathematics, SKU- Anantapuram, India

DOI:

https://doi.org/10.32628/IJSRSET207438

Keywords:

Semigroup, Normal, Seminormal, Regular, Semiregular, Quasinormal

Abstract

Semigroups being one of the algebraic structures are sets with associative binary operation defined on them. The theory of semigroups satisfy additional properties like commutative, Left(Right) cyclic i.e., L(R) cyclic , Left(Right) identity, Left(Right) cancellative and many others. In this paper we determine different structures of semigroups like normal, seminormal, quasinormal, semiregular and others by using the identity abc = ac with the concept of L(R) cyclic properties of semigroups.

References

  1. Howie, John Mackintosh. An introduction to semigroup theory. Vol. 7. Academic Pr, 1976.
  2. Clifford, Alfred Hoblitzelle, Arthur Hoblitzelle Clifford, and G. B. Preston. The algebraic theory of semigroups, Volume II. Vol. 7. American Mathematical Soc., 1961.
  3. Distler, Andreas. Classification and enumeration of finite semigroups. Diss. University of St Andrews, 2010.
  4. Reddy, U. Ananda, G. Shobhalatha, and L. Sreenivasulu Reddy. "Magma into Commutative Magma." Advances in Algebra 9.1 (2016): 31-36.
  5. U.Ananda Reddy, Dr.G.Shobhalatha, Dr.L.Sreenivasulu Reddy: L-Cyclic Magma versus R-Cyclic Magma, International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 4, Issue 8, August 2016, PP 1-6.
  6. D.D Padma Priya, G. Shobhalatha, and R. Bhuvana Vijaya. "Properties of semigroups in (semi-) automata." International Journal of Mathematics Trends and Technology 30.1 (2016): 43-47..
  7. Lidl, Rudolf, and Günter Pilz. Applied abstract algebra. Springer Science & Business Media, 2012.
  8. D.D. Padma Priya, Srinivasa G, G. Shobhalatha and R. Bhuvana Vijaya “ L(R) cyclic semigroups satisfying the identity abc= ca ” International Journal of Psychosocial Rehabilitation, ISSN: 1475-7192, Volume 24, Issue-5 , May 2020.

International Journal of Scientific Research in Science, Engineering and Technology

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Published

2020-08-30

Issue

Volume 7, Issue 4, July-August-2020

Section

Research Articles

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How to Cite

[1]
D. D. Padma Priya, G. Shobhalatha "L(R) Cyclic Semigroups Satisfying The Identity : abc = ac" International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 7, Issue 4, pp.146-150, July-August-2020. Available at doi : https://doi.org/10.32628/IJSRSET207438