STRONGLY DUO AND DUO RIGHT S-ACTS - Roueentan, Mohammad; Ershad, Majid (Italian Journal of Pure and Applied Mathematics, 2014)
New kinds of acts, namely strongly duo and duo acts over a monoid are introduced and investigated. This leads to the study of the relation between these kinds of acts and other classes of acts, such as injective, projective and multiplication. It is shown that a projective act is duo if and only if it is a multiplication act. In addition if S is commutative, then a cyclic S-act is strongly duo if and only if it is cyclic quasi-injective.