Kilp and Knauer in ( Communications In Algebra, 20(7), 1841-1856,1992) gave a characterizations of monoids when all generators in category of right S-acts (S is a monoid) satisfy properties such as freeness, projectivity, strong flatness, Condition (P), principal weak flatness, principal weak injectivity, weak injectivity, injectivity, divisibility, strong faithfulness, torsion freeness, and Sedaghtjoo in (Semigroup Forum, 87:653-662, 2013) gave a characterizations of monoids when all generators in category of right S-acts satisfy properties such as weak flatness, Condition (E) and regularity. To our knowledge, the problem has not been studied for properties mentioned above of (finitely generated, cyclic, monocyclic, Rees factor) right acts. In this article we answer the question corresponding to these properties and also fg-weak injectivity. |