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A semigroup S is called .E-inversive if for every a € S there is an x € S such that (ax) 1 = ax. A construction of all £-inversive subdirect products of two £-inversive semigroups is given using the concept of subhomomorphism introduced by McAlister and Reilly for inverse semigroups. As an application, E-unitary covers for an is-inversive semigroup are found, in particular for those whose maximum group homomorphic image is a given group. For this purpose, the explicit form of the least groupdoi:10.1017/s1446788700035199 fatcat:oyvqrmmcw5dbxgvlpxjk3db3te