Abstract
This paper is inspired by Mitsch, Petrich, Reilly’s work on E – inversive semigroups and inverse semigroups. We first introduce the notions of a good subdirect product and a good surjective subhomomorphism of of E – inversive abundant semigroups. After obtaining some characterizations of such semigroups, some structure theorems are established by using the notions of good subdirect products and good surjective subhomomorphisms, and necessary and sufficient conditions for good subdirect products of two E – inversive abundant semigroups to be again E – inversive abundant are given.
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