Strongly rpp semigroups endowed with some natural partial orders

Xiaowei Qiu, Xiaojiang Guo, K.P. Shum

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.


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Published: 2013-09-10

How to Cite this Article:

Xiaowei Qiu, Xiaojiang Guo, K.P. Shum, Strongly rpp semigroups endowed with some natural partial orders, J. Semigroup Theory Appl., 2013 (2013), Article ID 7

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.

Journal of Semigroup Theory and Applications

ISSN 2051-2937

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