The Translational Hull of a Left Restriction Semigroup

Ndubuisi R.U^1, and Udoaka O.G²

¹Department of Mathematics/Statistics, Hezekiah University, Nkwerre, Nigeria

²Department of Mathematics/ Statistics, Akwa Ibom State University, Ikot Akpaden, Nigeria

Cite this paper:
Ndubuisi R.U and Udoaka O.G. The Translational Hull of a Left Restriction Semigroup. American Journal of Mathematical Analysis. 2018; 6(1):1-4. doi: 10.12691/ajma-6-1-1

Abstract

In this paper, the translational hull of a left restriction semigroup is considered. We prove that the translational hull of a left restriction semigroup is still of the same type. This result extends the result of Guo and Shum on translational hulls of type A semigroups given in 2003.

Keywords:
translational hulls left adequate semigroups left restriction semigroups

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	M. Petrich. The translational hull in semigroups and rings. Semigroup Forum 1 (1970), 283-360.
[2]	J. E Ault. The translational hull of an inverse semigroup. Glasgow Math. J. 14 (1973), 56-64.
[3]	J. B. Fountain, G.M.S. Gomes and V. Gould. The free ample monoid. Int. j.Algebra comp., 19 (2009), 527-554.
[4]	G. Xiaojiang and K. P Shum. On translational hull of type A semigroups. J. Algebra 269 (2003), 240-249.
[5]	R.U Ndubuisi and O.G Udoaka. On left restriction semigroups. Intl j. Algebra and Statistics, Vol 5: 1(2016), 59-66.
[6]	V. Gould. Notes on restriction semigroups and related structures. http:// www-users.york.ac.uk / ~ Varg1/ finitela. Ps.
[7]	J. B. Fountain. Abundant semigroups, Proc. London. Math. Soc., (3) 44 (1982), 103-129.
[8]	J. B. Fountain. Adequate semigroups. Proc. Edinb. Math. Soc., 22(1979), 113-125.
[9]	Howie, J.M. Fundamentals of Semigroup Theory, Oxford University Press, Inc. USA, 1995.