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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机译：在本文中，我们研究了具有自然偏序的强rpp半群。我们首先考虑强rpp半群上的一些自然偏序，即$ leq_ {sl}， leq_ {sr} $和$ leq_ {s} $。然后，我们获得了上述自然偏序下强rpp半群的一些特征，我们还确定了超级rpp半群何时与自然偏序$ leq_ {sl} $兼容。先前由K. S. S. Nambooripad，M.给出的半群上自然偏序的一些已知结果。 V. Lawson，T. S. Blyth，Gracida M. S. Gomes，X. J. Guo和Y. F. Luo，以及X. J. Guo和K. P. Shum得到了充实和加强。
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