چكيده لاتين :
In this paper we investigate actions of a monoid of the form S = G⋃I, where G is a group and I is an ideal of S. So, naturally, every S-act can be considered as an I^1-act. The central question here is that what is the relation between weakly injective and divisible I^1-acts and weakly injective and divisible S-acts?
We are going to respond this question and show that, given an S-act A, (principally, finitely generated) weakly injective and divisible property of A is extendable from I^1-acts to S-acts in general. We also show that if I is strongly regular then an S-act A with a unique fixed element
θ is weakly injective if and only if A is injective relative to inclusion I ----> S. Also if I^1 is a left cancellable principal ideal monoid. Then, divisiblity of A as an I^1-act implies weakly injectivity of A as an S-act.
