ON QUASI NIL-INJECTIVE MODULES

Module M is called quasi nil-injective if for each m ∈ Nil(M) and each homomorphism f : mR → M , there exists a homomorphism f̄ : M → M such that f̄(x) = f(x) for every x ∈ mR. In this paper, we first obtain some characterizations of the class of quasi nil-injective modules and some known results can be deduced from these characteristics. Next, we apply to ring and obtain some properties of a quasi nil-injective rings. We proved that a ring R is semiprime if only if every right R-module (cyclic) is quasi nil-R-injective.