مجتبی صداقت جو

The work is an account on injectivity relative to the class of monomorphisms with indecomposable codomains in the category of acts over monoids. We establish that injective acts relative to this class, are the closest ones to their envelopes in the class of non-injective acts. We show that such acts are indeed, indecomposable components of injective acts. Besides, we show that injectivity relative to monomorphisms with indecomposable codomains is the same one relative to cyclic codomains.