Strongly rpp semigroups endowed with some natural partial orders
Abstract
In this paper we study the strongly rpp semigroups endowed with a natural partial order. We first consider some natural partial orders on a strongly rpp semigroup, namely $\leq_{sl}, \leq_{sr}$ and $\leq_{s}$. Then we obtain some characterizations of strongly rpp semigroups under the above natural partial orders, we also determine when will a super rpp semigroups be compatible with the natural partial order $\leq_{sl}$. Some known results on natural partial orders on semigroups previously given by K. S. S. Nambooripad,M. V. Lawson, T. S. Blyth, Gracida M. S. Gomes, X. J. Guo and Y. F. Luo, and X. J. Guo and K. P. Shum are enriched and strengthened.
- Published
- 10 September 2013
- Volume
- 2013 (2013)
- License
- CC BY 3.0
Copyright © 2013 Xiaowei Qiu, Xiaojiang Guo, K.P. Shum. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
X. Qiu, X. Guo, K. P. Shum, Strongly rpp semigroups endowed with some natural partial orders, J. Semigroup Theory Appl. 2013 (2013), 7.
BibTeX
@article{Qiu2013,
author = {Qiu, Xiaowei and Guo, Xiaojiang and Shum, K.P.},
title = {Strongly rpp semigroups endowed with some natural partial orders},
journal = {J. Semigroup Theory Appl.},
volume = {2013},
year = {2013},
pages = {7},
doi = {}
}