Suppose that R is a commutative ring with 1≠ 0. In this paper, we introduce the concept of 2-
absorbing ideal which is a generalisation of prime ideal. A nonzero proper ideal I of R is …

This paper deals with well-known extensions of the Prüfer domain concept to arbitrary
commutative rings. We investigate the transfer of these notions in trivial ring extensions (also …

Bruce Olberding Department of Mathematical Sciences, New Mexico State University, Las
Cruces, New Mexico 88003-8001, USA olberdin@ emmy. nmsu. edu12. 1 …

In a paper of 1978 N. Vaughan and R. Yeagy prove that if a domain R has the property that
every proper ideal is a product of radical ideals, then R is an almost Dedekind domain; that …

An ideal of a ring is completely irreducible if it is not the intersection of any set of proper
overideals. We investigate the structure of completely irrreducible ideals in a commutative …

An intersection of sets A= ⋂ _ i ∈ I B_i A=⋂ i∈ IB i is irredundant if no B_i B i can be omitted
from this intersection. We develop a topological approach to irredundance by introducing a …

Let H be an integral domain, and let Σ be a collection of integrally closed overrings of H. We
show that if A is an overring of H such that, and if Σ is a Noetherian subspace of the space of …

Throughout this paper all rings are commutative with nonzero identity comma and all
modules are considered to be unitary period We wish to study properties of submod hyphen …

An ideal of a commutative ring is completely irreducible if it is not the intersection of any set
of proper overideals. It is known that every ideal is an intersection of completely irreducible …

This article introduces and advances the basic theory of “uniformly primary ideals” for
commutative rings, a concept that imposes a certain boundedness condition on the usual …