Co-EP-Ness and EP-Ness Involving the Inverse along an Element

Honglin Zou (), Dijana Mosić and Huihui Zhu
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Honglin Zou: College of Basic Science, Zhejiang Shuren University, Hangzhou 310015, China
Dijana Mosić: Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia
Huihui Zhu: School of Mathematics, Hefei University of Technology, Hefei 230009, China

Mathematics, 2023, vol. 11, issue 9, 1-15

Abstract: Let a , d be two elements in rings and a ∥ d be the inverse of a along d . When a ∥ d exists, we obtain several characterizations for the invertibility of a a ∥ d − a ∥ d a , which is related to the invertibility of elements expressed by certain functions of a , d and suitable elements from the center of the ring. On the other hand, some equivalent conditions for the equality a a ∥ d = a ∥ d a , as the complement of the previous invertibility in some sense, are given by means of the group inverses and the ring units, respectively. Then, the results obtained are applied in a ∗ -ring, namely, when d = a ∗ , the co-EP and EP properties are deduced correspondingly.

Keywords: ring; invertibility; inverse along an element; co-EP elements; EP elements (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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