In this paper, we analyze some results on ideal theory of commutative semirings with non-
zero identity analogues to commutative rings with non-zero identity. Here we will make an …

Can there be a structure space-type theory for an arbitrary class of ideals of a ring? The
ideal spaces introduced in this paper allows such a study and our theory includes (but not …

A proper ideal I of a ring R is said to be strongly irreducible if for each pair of ideals A and B
of R, implies that either or. In this paper we study strongly irreducible ideals in different rings …

Let M be a non-zero module over an associative (not necessarily commutative) ring. In this
paper, we investigate the so-called second and coprime submodules of M. Moreover, we …

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 …

We generalize the notion of comaximal factorization of ring ideals to the language of weak
ideal systems on monoids and prove several results generalizing and extending previous …

An ideal I of a commutative ring R is said to be irreducible if it cannot be written as the
intersection of two larger ideals. A proper ideal I of a ring R is said to be strongly irreducible …

This paper is motivated by the results in [6]. We study some properties of strongly irreducible
submodules of a module. In fact, our objective is to investigate strongly irreducible modules …

Let $ R $ be a commutative ring. The purpose of this article is to introduce a new class of
ideals of R called weakly irreducible ideals. This class could be a generalization of the …

Some Remarks on Strongly Irreducible Ideals 1 Introduction Page 1 Journal of Mathematical
Extension Vol. 18, No. 6, (2024) (5)1-14 URL: https://doi.org/10.30495/JME.2024.3134 ISSN …