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Publication Type : Journal Article
Publisher : International journal of Engineering and Technology
Source : International journal of Engineering and Technology, vol. 7, no. 2.13, pp. 306-308, 2018
Url : https://www.sciencepubco.com/index.php/ijet/article/view/12788
Campus : Amritapuri
School : School of Arts and Sciences
Department : Mathematics
Year : 2018
Abstract : Let S be a unit regular semigroup with group of units G = G(S) and semilattice of idempotents E = E(S). Then for every there is a such that Then both xu and ux are idempotents and we can write or .Thus every element of a unit regular inverse monoid is a product of a group element and an idempotent. It is evident that every L-class and every R-class contains exactly one idempotent where L and R are two of Greens relations. Since inverse monoids are R unipotent, every element of a unit regular inverse monoid can be written as s = eu where the idempotent part e is unique and u is a unit. A completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. A Clifford semigroup is a completely regular inverse semigroup. Characterization of unit regular inverse monoids in terms of the group of units and the semilattice of idempotents is a problem often attempted and in this direction we have studied the structure of unit regular inverse monoids and Clifford monoids.
Cite this Research Publication : Dr. Sreeja V. K., “Unit Regular Inverse Monoids and Clifford Monoids (UAE)”, International journal of Engineering and Technology, vol. 7, no. 2.13, pp. 306-308, 2018