Add to ORKGAbstract. LetM be a finitely-generated module over a Noetherian ring R. Suppose a is an ideal of R and let N = aM and b = Ann(M/N). If b ⊆ J(R), M is complete with respect to the b-adic topology, {Pi}i≥1 is a countable family of prime submodules of M, and x ∈M, then x+N ⊆ ⋃i≥1Pi implies that x+N ⊆ Pj for some j ≥ 1. This extends a theorem of Sharp and Vámos concerning prime ideals to prime submodules. 2000 Mathematics Subject Classification. 13C99, 13J10, 13E05
For a submodule $N$ of an $R$-module $M$, a unique product of prime ideals in $R$ is assigned, which...
Abstract. Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...
Abstract. LetM be a finitely-generated module over a Noetherian ring R. Suppose a is an ideal of R a...
Abstract. LetM be a finitely-generated module over a Noetherian ring R. Suppose a is an ideal of R a...
Let M be a finitely-generated module over a Noetherian ring R. Suppose a is an ideal of R and let N ...
If M is a torsion-free module over an integral domain, then we show that for each submodule N of M t...
Let $R$ be a commutative ring with identity, and $n\geq 1$ an integer. A proper submodule $N$ o...
Let R be a commutative ring with identity and let M be a unitary R-module. Let S(M) be the set of al...
AbstractLetAbe a Noetherian ring,ĨandIbe comaximal ideals ofA, andPbe a projectiveA-module. “Additio...
summary:We investigate some properties of $n$-submodules. More precisely, we find a necessary and su...
Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that...
Our main aim in this note, is a further generalization of a result due to D. D. Anderson, i.e., it i...
In this paper, we prove that a finitely embedded $R$-module $M$ is Artinian if and only if for every...
Prime submodule is the abstraction to module theory of prime ideal in ring theory. A proper submodu...
For a submodule $N$ of an $R$-module $M$, a unique product of prime ideals in $R$ is assigned, which...
Abstract. Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...
Abstract. LetM be a finitely-generated module over a Noetherian ring R. Suppose a is an ideal of R a...
Abstract. LetM be a finitely-generated module over a Noetherian ring R. Suppose a is an ideal of R a...
Let M be a finitely-generated module over a Noetherian ring R. Suppose a is an ideal of R and let N ...
If M is a torsion-free module over an integral domain, then we show that for each submodule N of M t...
Let $R$ be a commutative ring with identity, and $n\geq 1$ an integer. A proper submodule $N$ o...
Let R be a commutative ring with identity and let M be a unitary R-module. Let S(M) be the set of al...
AbstractLetAbe a Noetherian ring,ĨandIbe comaximal ideals ofA, andPbe a projectiveA-module. “Additio...
summary:We investigate some properties of $n$-submodules. More precisely, we find a necessary and su...
Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that...
Our main aim in this note, is a further generalization of a result due to D. D. Anderson, i.e., it i...
In this paper, we prove that a finitely embedded $R$-module $M$ is Artinian if and only if for every...
Prime submodule is the abstraction to module theory of prime ideal in ring theory. A proper submodu...
For a submodule $N$ of an $R$-module $M$, a unique product of prime ideals in $R$ is assigned, which...
Abstract. Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime...
Let M be a module over a ring R, which satisfies the ascending chain condition on submodules of the ...