Construction of Inverse Unit Regular Monoids from a Semilattice and a Group

  • Authors

    • Sreeja V.K
    https://doi.org/10.14419/ijet.v7i4.36.24927

    Received date: December 28, 2018

    Accepted date: December 28, 2018

    Published date: December 9, 2018

  • Inverse monoids, Unit regular monoids, Semi lattice, group

  • Abstract

    This paper is a continuation of a previous paper [6] in which the structure of certain unit regular semigroups called R-strongly unit regular monoids has been studied. A monoid S is said to be unit regular if for each element s Î S there exists an element u in the group of units G of S such that s = sus. Hence where su is an idempotent and is a unit. A unit regular monoid S is said to be a unit regular inverse monoid if the set of idempotents of S form a semilattice. 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. Here we give a detailed study of inverse unit regular monoids and the results  are mainly based on [10]. The relations between the semilattice of idempotents and the group of units in unit regular inverse monoids are better identified in this case.

  • References

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  • How to Cite

    V.K, S. (2018). Construction of Inverse Unit Regular Monoids from a Semilattice and a Group. International Journal of Engineering and Technology, 7(4.36), 950-952. https://doi.org/10.14419/ijet.v7i4.36.24927