  Starting from the definition of A-Fredholm and semi-A-Fredholm operator on
the standard module over a unital C*- algebra A, introduced in [8] and [4], we
construct various generalizations of these operators and obtain several results
as an analogue or a generalization of the results in [1], [2], [3],[7].
Moreover, we study also non-adjointable semi-A-Fredholm operators as a natural
continuation of the work in [6] on non-adjointable A-Fredholm operators and
obtain an analogue or a generalization in this setting of the results in [4],
[5].
