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

• ## Authors

• Sreeja V.K
2018-12-09
• 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 ÃŽ 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 resultsÂ  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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• ## References

1. [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 653â€“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), â€œ A study of unit regular semigroupsâ€(Ph. d Thesis), University of Kerala, Department of Mathematics, Kerala, India

• ## How to Cite

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

Received date: 2018-12-28

Accepted date: 2018-12-28

Published date: 2018-12-09