Related papers: Prime subcomplexes
In this paper, we will introduce two generalizations of second submodules of a module over a commutative ring and explore some basic properties of these classes of modules.
Consider the Fourier expansions of two elements of a given space of modular forms. How many leading coefficients must agree in order to guarantee that the two expansions are the same? Sturm gave an upper bound for modular forms of a given…
In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which…
In this study, all rings are commutative with non-zero identity and all modules are considered to be unital. Let $M$ be a left $R$-module. A proper submodule $N$ of $M$ is called an $S$-$weakly$ $prime$ submodule if $0_{M}\neq f(m)\in N$…
Let R be a commutative ring with unity and M be an R- module In this paper we introduce semi n- absorbing and (k, n)-closed submodules of modules over commutative rings, and investigate their basic properties.
The group of singular elements was first introduced by Helmut Hasse and later it has been studied by numerous authors including such well known mathematicians as: Cassels, Furtw\"{a}ngler, Hecke, Knebusch, Takagi and of course Hasse…
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…
The aim of this paper is to investigate properties of endo-prime and endo-coprime modules which are generalizations of prime and simple rings, respectively. Various properties of endo-coprime modules are obtained. Duality-like connections…
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 Central sets theorem was first introduced by H. Furstenberg [F] in terms of Dynamical systems. Later Hindman and Bergelson extended the theorem using Stone-$\v{C}$ech compactification $\beta$$\mathbb{N}$ of $\mathbb{N}$. In [SY]…
The set of the first Hilbert coefficients of parameter ideals relative to a module--its Chern coefficients--over a local Noetherian ring codes for considerable information about its structure--noteworthy properties such as that of…
In the present paper, modules over integral domains and principal ideal domains that are proper essential extensions of some submodules are classified. We introduce a new class of modules that we call $\mathrm{SM}$ modules and show that the…
Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. The aim of this paper is to introduce the notion of S-secondary submodules of M as a generalization of secondary submodules of…
Primary decomposition is a very important tool of commutative algebra and geometry. In this paper we generalized some of the existing algorithms of primary decomposition developed by Eisenbud et al. (cf. [EHV]) for free modules and also…
In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the…
Translated from the Latin original "Facillima methodus plurimos numeros primos praemagnos inveniendi" (1778). E718 in the Enestrom index. If m is a number of the form 4k+1 and is a sum of two relatively prime squares, then it is prime if…
Projective modules play an important role in the study of the category of modules over rings and in the characterization of various classes of rings. Several characterizations of projective objects which are equivalent for modules over…
Let $X$ be a set of positive integers, and let $\mathbb Z_K$ be the ring of integers of a number field $K$ of degree $n$. Denote by $N(I)$ the absolute norm of an ideal $I$ of $\mathbb Z_K$, and by $\mathcal A$ the set of principal ideals…
For commutative rings with identity, we introduce and study the concept of semi $r$-ideals which is a kind of generalization of both $r$-ideals and semiprime ideals. A proper ideal $I$ of a commutative ring $R$ is called semi $r$-ideal if…
We explore some concepts of module theory that derive from the notion of primeness, such as first modules, and extend them to more general environments. We also provide descriptions of simple left semiartinian rings, left local rings,…