Abstract
Let R be a unital -ring and let with e,f invertible Hermitian elements. In this paper, we define two types of outer generalized inverses, called pseudo e-core inverses and pseudo f-dual core inverses. An element is pseudo e-core invertible if there exist an element and some positive integer n such that and . Dually, a is pseudo f-dual core invertible if there exist an element and some positive integer m such that xax=x, and . Moreover, we investigate both of them for their characterizations and properties. Also, the relations between the pseudo e-core inverse (resp. the pseudo f-dual core inverse) and the inverse along an element are given.
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