We present an answer to a problem raised by Anderson and Chun in [DD Anderson and S.
Chun, Annihilator conditions on modules over commutative rings, J. Algebra Appl. 16 …

The main purpose of this paper is to generalize a result of TG Lucas which states that if R is
a reduced commutative ring and M is a flat R-module, then the idealization R⋉ M is an A …

In this paper we show that if {Ri} i∈ I is a family of commutative rings and {Mi} i∈ I is a family
of modules such that each Mi is an Ri-module, then the direct product Mi is a-module over Ri …

Let 𝑅 be a commutative ring and 𝑀 an 𝑅-module. Nagata introduced the idealization 𝑅 (+) 𝑀
of 𝑀. Here 𝑅 (+) 𝑀= 𝑅⊕ 𝑀 (direct sum) is a commutative ring with product (𝑟₁, 𝑚₁)(𝑟₂ …

Let R be a commutative ring and M an R-module. Let Z (M)={r∈ R| rm= 0 for some nonzero
m∈ M} and T (M)={m∈ M| rm= 0 for some nonzero r∈ R}. M satisfies Property A …

All rings are commutative with identity and all modules are unital. Anderson proved that a
submodule N of an R-module M is multiplication (resp. join principal) if and only if 0 (+) N is …

Abstract Let R⊆ Q be rings such that the inclusion φ: R→ Q is an epimorphism in the
category of rings and Q is flat both as a right and as a left R-module. Assume that F. dim …

It is shown that if every prime ideal minimal over an ideal I is finitely generated, then there
are only finitely many prime left ideals minimal over I. This immedeately generalizes Cohen's …

1. Introduction. Let R be a commutative ring with identity, let M be a unitary module over R,
and let a be an infinite cardinal. Following the terminology of universal algebra [5],[3], we call …

Let R be a commutative ring with identity. We will say that an R-module M has Nakayama
property, if IM= M, where I is an ideal of R, implies that there exists a∈ R such that aM= 0 …