Abstract:
In this talk, we introduce a new notion in a semigroup S as an extension of Mary's inverse. An existence criterion of this type inverse is derived 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. Then, a notion called left (resp. right) *-regular is given in *-semigroup. Moreover, we prove that a is Moore-Penrose invertible if and only if it is left *-regular if and only if it is right *-regular. We also consider the reverse order law for the inverse along an element. |