On Some Classes of Regular Semigroups
DOI:
https://doi.org/10.62054/ijdm/0103.09Keywords:
Generalized inverse semigroups, Idempotent, Locally inverse semigroups, Orthodox Semigroup, Regular semigroupsAbstract
In this paper we study and analyze the relationships between some special classes of regular semigroups, namely: Generalized inverse semigroups, Orthodox semigroups and locally inverse semigroups based on their idempotent properties. We then use an example to prove that every locally inverse semigroup is not a generalized inverse semigroup, thus validating the statement; “A generalized inverse semigroup has the property of being locally inverse. However, not every locally inverse semigroup is a generalized inverse semigroup.”
References
Guo, Y. (2008). A note on locally inverse semigroups algebras.International Journal of Mathematics and Mathematical Sciences. Article ID 576061, 5 pages doi:10.1155/2008/576061
Green, J. A. (1951). On the structure of semigroups. Annals of Mathematics. Second Series, 54(1), 163-172.
Garba, G. U. (2019). An overview of products of idempotents and nilpotents in finite semigroups of transformations. A seminal Paper Presented at The Quarterly Algebra Colloquium, National Mathematical Center, Abuja.
Howie, J. M. (1995). Fundamentals of semigroup theory. London Math. Soc. Monographs, New Series, 12. Oxford University Press, London.
Indhira, K. andChandrasekaran, V. M. (2011). Construction of generalized inverse semigroups. International Journal of Algebra, 5(15), 739-746.
Julie T., Indhira, K. and Chandrasekaran (2018). A study on regular semigroups and its idempotents. International Journal of Engineering and Technology, 7 (4.10), 511-513 https://doi.org/10.14419/ijet.v7i4.10.21214
Preston, G. B. (1954). Inverse semigroups. Journal of the London Mathematical Society. 29(4),
-403.https://doi.org/10.1112/jlms/s1-29.4.396
Yamada, M. (1967). Regular semigroups whose idempotents satisfy permutation identity.Pacific journal of mathematics, 21(2): 371-392.
Hall, T. E., (1969). On regular semigroups whose idempotents form a subsemigroup. Bull. Austral.Math. Soc. 1, 195-208
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