Related papers: Graded Classical Weakly Prime Submodules over Non-…

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.

Commutative rings in which every prime ideal is the intersection of maximal ideals are called Hilbert (or Jacobson) rings. We propose to define classical Hilbert modules by the property that {\it classical prime} submodules are the…

In this paper, we introduce and investigate \emph{semicorings} over associative semirings and their categories of \emph{semicomodules.} Our results generalize old and recent results on corings over rings and their categories of comodules.…

Weak proregularity of an ideal in a commutative ring is a subtle generalization of the noetherian property of the ring. Weak proregularity is of special importance for the study of derived completion, and it occurs quite often in…

The aim of this paper is to describe the classes of strongly flat and weakly cotorsion modules with respect to a multiplicative subset or a finite collection of multiplicative subsets in a commutative ring. The strongly flat modules are…

In a previous article (see \cite{CNP}), we introduced and analyzed ring-theoretic properties of object unital $\mathcal{G}$-graded rings $R$, where $\mathcal{G}$ is a groupoid. In the present article, we analyze the category $\grmod$ of…

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.

Let $R$ be a ring and $n$, $k$ two non-negative integers. In this paper, we introduce the concepts of $n$-weak injective and $n$-weak flat modules and via the notion of special super finitely presented modules, we obtain some…

Let R be a commutative ring, M an R-module. In this paper, we will introduce the concept of n-pure submodules of M as a generalization of pure submodules and obtain some related results.

The purpose of this note is to introduce primitive ideals of noncommutative semigroups and study some topological aspects of the corresponding structure spaces.

We count the number of submodules of an arbitrary module over a countable noetherian commutative ring. We give, along the way, a structural description of meager modules, which are defined as those that do not have the square of a simple…

The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduced the dual notion of z-submodules of M and some of extensions. Moreover, we investigate some properties of these classes of modules…

We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields and exterior algebras on one generator over…

A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the `base algebras') are shown to carry coseparable co-Frobenius coalgebra…

In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these…

Let R be a commutative ring with identity. We investigate some ring-theoretic properties of weakly Laskerian R-modules. Our results indicate that weakly Laskerian rings behave as Noetherian ones in many respects. However, we provide some…

Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The…

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…

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The aim of this paper is to introduce the notion of fully S-idempotent modules as a generalization of fully idempotent modules and investigate some…