Related papers: On (k,n)-closed submodules
In this paper we study and investigate concerning dependent elements of semiprime rings and prime rings R by using generalized derivation and derivation,when R admsit to satisfy some conditions,we give some results about that.
In this paper, we prove prime avoidance for ringoids. We also generalize McCoy's and Davis' prime avoidance theorems in the context of semiring theory. Next, we proceed to define and characterize compactly packed semirings and show that a…
Examples are given to show that the support of a complex of modules over a commutative noetherian ring may not be read off the minimal semi-injective resolution of the complex. The same examples also show that a localization of a…
We propose the use of quantum dots formed in a semiconductor nanocolumn for the realization of charge or spin based quantum bits. The radial carrier confinement is achieved by employing conformal overgrowth, while multiple segmented gates…
This paper examines various kinds of subspaces of the non-commutative spaces that are modelled on quasi-projective commutative schemes. It is shown how intersections and unions of weakly closed subspaces, closed subspaces, their weakly open…
The aim of this paper is to study the topological properties of some classes of subsemimodules endowed with a subbasis closed-set topology. We show that such spaces are $T_0$. When the semimodule is finitely generated, those spaces are…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…
In this paper, we classify certain subcategories of modules over a ring R. A wide subcategory of R-modules is an Abelian subcategory of R-Mod that is closed under extensions. We give a complete classification of wide subcategories of…
In this paper, we study the class of modules have the property that every pure submodule is essential in a direct summand. These modules are termed as pure extending modules which is a proper generalisation of extending modules. Examples…
Let $S$ be a semiring. An $S$-semimodule $M$ is called a multiplication semimodule if for each subsemimodule $N$ of $M$ there exists an ideal $I$ of $S$ such that $N=IM$. In this paper we investigate some properties of multiplication…
In this paper, we introduce the concepts of strongly 2-absorbing primary ideals (resp., submodules) and strongly 2-absorbing ideals (resp., submodules) as generalizations of strongly prime ideals. Furthermore, we investigate some basic…
Let $N$ be a submodule of a finitely generated module $M$ over a Noetherian ring. A method for the computation of the submodule generated by the envelope of $N$ is given. The relations between weakly prime submodules and their envelopes are…
In this paper, we introduce multiplicative semiderivation and we investigate the commutativity of semiprime rings satisfying certain conditions and identities involving multiplicative semiderivations on a nonzero ideal I of a ring R.
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…
It is well-known that a class of all modules, which are torsion-free with respect to a set of ideals, is closed under injective envelopes. In this paper, we consider a kind of a dual to this statement - are the divisibility classes closed…
A finitely generated module $M$ over a commutative Noetherian ring $R$ is called an $I$-Cohen Macaulay module, if \[ \grade(I,M) + \dim(M/IM)= \dim(M), \] where $I$ is a proper ideal of $R$. The aim of this paper is to study the structure…
For natural numbers $n$ and $k$, the concepts of $n$-modularly embedded subgroup, $k$-submodular subgroup and $k$-$\mathrm{LM}$-group are given, which generalize, respectively, the concepts of modular subgroup, submodular subgroup and…
In this note, we investigate the Baer splitting problem over commutative rings. In particular, we show that if a commutative ring $R$ is $\tau_q$-semisimple, then every Baer $R$-module is projective.
Given a semiprime Goldie module $M$ projective in $\sigma[M]$ we study decompositions on its $M$-injective hull $\hat{M}$ in terms of the minimal prime in $M$ submodules. With this, we characterize the semiprime Goldie modules in…
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…