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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Honglin Zou & Dijana Mosić & Huihui Zhu, 2023. "Co-EP-Ness and EP-Ness Involving the Inverse along an Element," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2026-:d:1131812
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