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

 
 
 
  • Abstract
  • Keywords
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  • 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.

     

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  • Keywords


    Inverse monoids, Unit regular monoids, Semi lattice, group

  • References


      [1] 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. Math. 4 653–670 (2011).

      [2] Chen S.Y. and S.C. Hsieh, Factorizable inverse semigroups, Semigroup forum Vol 8(1974), 283 -297

      [3] Clifford A.H and Preston G.B., The algebraic theory of semigroups, Surveys of the American Mathematical society 7, Providence, 1961.

      [4] Hickey J.B and M.V. Lawson, Unit regular monoids, University of Glasgow, Department of Mathematics.

      [5] Nambooripad K.S.S. , Structure of Regular semigroups 1, Mem. Amer. Math. soc, 224, November 1979.

      [6] Nambooripad K.S.S., The natural partial order on a regular semigroup, Proc. Edinburgh Math. Soc (1980), 249-260.

      [7] T.S. Blyth and Mc Fadden , Unit orthodox semigroups, Glasgow Math.J.24 (1983), 39-42

      [8] V.K. Sreeja and A.R.Rajan, Construction of certain unit regular orthodox submonoids Southeast Asian Bulletin of Mathematics, (2014 ) 38 (4): 907-916

      [9] V.K. Sreeja and A.R.Rajan, Some properties of regular monoids, Southeast Asian Bulletin of Mathematics, (2015 ) 39 (6): 891-902

      [10] V.K.Sreeja (2004), “ A study of unit regular semigroups”(Ph. d Thesis), University of Kerala, Department of Mathematics, Kerala, India


 

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Article ID: 24927
 
DOI: 10.14419/ijet.v7i4.36.24927




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