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 families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

Cofiniteness of the generalized local cohomology modules $H^{i}_{mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ with respect to an ideal $mathfrak{a}$ is studied for some $i^{,}s$ witha specified property. Furthermore, Artinianness of $H^{j}_{mathfrak{b}_{0}}(H_{mathfrak{a}}^{i}(M,N))$ is investigated by using the above result, in certain graded situations, where $mathfrak{b}_{0}$ is an idea...

We prove that each ideal of a locally formally equidimensional analytically un-ramiied Noetherian integral domain is the contraction of an ideal of a one-dimensional semilo-cal birational extension domain. We give an application to a problem concerning the primary decomposition of powers of ideals in Noetherian rings. It is shown in S2] that for each ideal I in a Noetherian commutative ring R t...

In this paper we describe the method which applied to successfully compute primary decomposition of a certain ideal coming from applications in combinatorial algebra and algebraic statistics regarding conditional independence statements with hidden variables. While our is based on algorithm for by Gianni, Trager Zacharias, were not able decompose using standard form that algorithm, nor any othe...

In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...