Open AccessUnit regular inverse monoids and Cliford monoids
Author(s) -
V K Sreeja
Publication year - 2018
Publication title -
international journal of engineering and technology
Language(s) - English
Resource type - Journals
ISSN - 2227-524X
DOI - 10.14419/ijet.v7i2.13.12788
Subject(s) - mathematics , inverse element , semilattice , idempotence , monoid , inverse semigroup , bicyclic semigroup , unit (ring theory) , semigroup , inverse , element (criminal law) , group (periodic table) , unipotent , cancellative semigroup , combinatorics , regular semigroup , pure mathematics , algebra over a field , discrete mathematics , special classes of semigroups , geometry , chemistry , mathematics education , organic chemistry , political science , law
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.