Naturally Ordered Abundant Semigroups for which each Idempotent has a Greatest Inverse

Xiaojiang Guo, K.P. Shum

Abstract

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-regular and reflexive naturally ordered abundant semigroups each of whose idempotents has a greatest inverse are studied. In this paper, we give a construction theorem for such ordered semigroups. Our theorem extends a previous structure theorem on naturally ordered abundant semigroups of X.J. Guo and X.Y. Xie [13]. Some other results related to naturally ordered regular semigroups areamplified and strengthened.

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