Provides a picture of the research that has occurred and the techniques that have been
involved in studying Prufer domains since about 1970. The text covers generating ideals in …

We extend the definition of a finite conductor domain to rings with zero divisors, and develop
a theory of these rings which allows us, among other things, to provide examples of non …

The rings considered in this article are commutative with identity. This article is motivated by
the results proved by Hamed and Malek (Beitr Algebra Geom 61: 533–542, 2020) on S …

Our goal is to establish an efficient decomposition of an ideal $ A $ of a commutative ring $
R $ as an intersection of primal ideals. We prove the existence of a canonical primal …

Let R be a commutative ring with identity, M an R-module and S⊆ R a multiplicative set.
Then M is called S-finite if there exist an s∈ S and a finitely generated submodule N of M …

Let M be a module over a ring R, which satisfies the ascending chain condition on
submodules of the form N: B⊆ N: B 2⊆ N: B 3⊆⋯ for every submodule N of M and every …

Let M be a module over a commutative ring R. A submodule P of M is called prime if P≠ M
and, whenever r∈ R, e∈ M, and re∈ P, we have rM⊆ P or e∈ P. We let Spec (M) denote …

A Q-ring is a commutative ring in which every ideal is a product of primary ideals. We show
that R is a Q-ring if and only if R is a Laskerian ring (every ideal has a primary …

This article centers around artinianness of the local cohomology of ZD-modules. Let a he an
ideal of a commutative Noetherian ring R. The notion of a-relative Goldie dimension of an R …

A commutative ring with unity “has n-acc” iff every ascending chain of n-generated ideals
stabilizes. This paper shows that any polynomial ring or formal power series ring over a …