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.