Unit regular inverse monoids and Cliford monoids

 
 
 
  • Abstract
  • Keywords
  • References
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  • 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.

     


  • Keywords


    Inverse Monoids; Unit Regular Monoids; Clifford Monoids; Green’s Relation.

  • References


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      [3] Nambooripad K.S.S., The natural partial order on a regular semigroup, Proc. Edinburgh Math. Soc (1980), 249-260. https://doi.org/10.1017/S0013091500003801.

      [4] A.R. Rajan and V.K. Sreeja, Construction of a R-strongly unit regular Monoid from a regular Biordered set and a group, Asian-Eur. J. Ma.

      [5] Mahdi Fakoor, Amirreza Kosari, Mohsen Jafarzadeh, Revision on fuzzy artificial potential field for humanoid robot path planning in unknown environment, International Journal of Advanced Mechatronic Systems, Volume 6, Issue 4, page 174-183, 2015. https://doi.org/10.1504/IJAMECHS.2015.072707.

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Article ID: 12788
 
DOI: 10.14419/ijet.v7i2.13.12788




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