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Keigher showed that quasi-prime ideals in differential commutative rings are analogues of prime ideals in commutative rings. In that direction, he introduced and studied new types of differential rings using quasi-prime ideals of a differential ring. In the same sprit, we define and study two new types of differential rings which lead to the mirrors of the corresponding results on von Neumann r...

in this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. in particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over noetherian rings are proved. moreover, w...

Let R be an arbitrary ring with identity. In this paper, we introduce quasi-reduced rings as a generalization of reduced rings and investigate their properties. The ring R is called quasi-reduced if for any a, b ∈ R, ab = 0 implies (aR) ∩ (Rb) is contained in the center of R. We prove that some results of reduced rings can be extended to quasi-reduced rings for this general settings. 2010 Mathe...