Abstract
In this paper, we introduce a new notion in a semigroup as an extension of Mary’s inverse. Let . An element is called left (resp. right) invertible along if there exists such that (resp. ) and (resp. ). An existence criterion of this type inverse is derived. Moreover, several characterizations of left (right) regularity, left (right) -regularity and left (right) -regularity are given in a semigroup. Further, another existence criterion of this type inverse is given by means of a left (right) invertibility of certain elements in a ring. Finally, we study the (left, right) inverse along a product in a ring, and, as an application, Mary’s inverse along a matrix is expressed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
