Related papers: Some generalizations of strongly prime ideals
In this article, we study the primary decomposition of some binomial ideals. In particular, we introduce the concept of polyocollection, a combinatorial object that generalizes the definitions of collection of cells and polyomino, that can…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
We give an introduction to the theory of initial ideals and initial algebras with emphasis on the transfer of structural properties.
We introduce the concept of constructible ideal and we relate this concept with the notion of constructible simplicial complex. Several properties of constructible ideals are studied.
In this paper we extend the characterisation of kernels in semirings as subtractive ideals to general algebras. We then analyse the counterparts of ``subtractive'' and ``ideal'' in several different algebraic settings.
In this paper, all rings are commutative with nonzero identity. Let M be an R-module. We introduce the concept of phi classical 1-absorbing prime submodules. A proper submodule N of M is a phi classical 1-absorbing prime submodule if…
The goal of this article is to propose and examine the notion of graded classical weakly prime submodules over non-commutative graded rings which is a generalization of the concept of graded classical weakly prime submodules over…
For a commutative unital ring $R$ with fixed ideals $I$ and $J$, we introduce and study $I$-prime $R$-modules and $(I, J)$-prime $R$-modules together with their duals $I$-coprime $R$-modules and $(I,J)$-coprime $R$-modules respectively. We…
Let $R$ be a commutative ring with identity. For a finitely generated $R$-module $M$, the notion of associated prime submodules of $M$ is defined. It is shown that this notion inherits most of essential properties of the usual notion of…
In this paper we introduce the notion of admissible skein modules associated to an ideal in a pivotal category. We explain how these modules are generalizations of the Kauffman skein algebra and how they relate to renormalized quantum…
All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classification of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of…
In this paper, we introduce $\phi$-1-absorbing prime ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity $1\neq0$ and $\phi:\mathcal{I}(R)\rightarrow\mathcal{I}(R)\cup\{\emptyset\}$ be a function where…
Ideals generated by adjacent 2-minors are studied. First, the problem when such an ideal is a prime ideal as well as the problem when such an ideal possesses a quadratic Gr\"obner basis is solved. Second, we describe explicitly a primary…
The principal result is a primary decomposition of ideals generated by the (2x2)-subpermanents of a generic matrix. These permanental ideals almost always have embedded components and their minimal primes are of three distinct heights. Thus…
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. The aim of this paper is to extend the notion of quasi $J$-ideals of commutative rings to quasi $J$-submodules of modules. We call a proper submodule $N$ of $M$ a…
We present combinatorial characterizations for the associated primes of the second power of squarefree monomial ideals and criteria for this power to have positive depth or depth greater than one.
Let $R$ be a commutative ring with nonzero identity. A. Yassine et al. defined in the paper (Yassine, Nikmehr and Nikandish, 2020), the concept of $1$-absorbing prime ideals as follows: a proper ideal $I$ of $R$ is said to be a…
Following the structure theory approach for rings, the aim of this paper is to study some distinguished classes of Lie algebras. We introduce the notion of a Lie-module and discuss some relations of it with various classes of ideals of a…
In this paper, our purpose is to introduce and study the notion of weakly n-ary S-primary hyperideals in a commutative Krasner (m,n)-hyperring.
The notion off-ideals is recent and has been studied in the papers[1] [2], [5], [10], [11], [12], [13], [14] and [15]. In this paper, we have generalized the idea off-ideals to quasi f-ideals. This extended class of ideals is much bigger…