L (R) Cyclic Semigroups Satisfying the Identity: abc = ca
DOI:
https://doi.org/10.61841/8d433e88Keywords:
Semigroup, Normal, Seminormal, Regular, Semiregular, QuasinormalAbstract
Semigroups, being one of the algebraic structures, are sets with an associative binary operation defined on them. The theory of semigroups satisfies additional properties like commutativity, 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 = c with the concept of L(R) cyclic properties of semigroups.
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[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] Priya, DD Padma, 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, G. Shobhalatha, U. Nagireddy, and R. Bhuvana Vijaya, “Relations on semigroups.”
International Journal of Research, Engineering and Management (IJREAM). Vol-04, Issue-09, Dec-2018.
[9] Holambe, T.L., and Mohammed Mazhar-ul-Haque. "A remark on semigroup property in fractional calculus." International Journal of Mathematics and Computer Applications Research (IJMCAR) 4.6 (2014): 27-32.
[10] Gaikwad, Vasant, and Ms Chaudhary. "Zak Transform for Boehmians." International Journal of Applied Mathematics & Statistical Sciences (IJAMSS) 2.3 (2013): 33-40
[11] Anitha, B. "Intuitionistic Fuzzy Ideals." International Journal of Mathematics and Computer Application Research (IJMCAR) 9.2 (2019): 63–72.
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