Related papers: $\phi$-$\delta$-$S$-primary submodule

In this paper, we introduce the notion of uniformly S-pseudo-projective (u-S-pseudo-projective) modules as a generalization of u-S-projective modules. Let R be a ring and S a multiplicative subset of R. An R-module P is said to be…

Let {\phi} be a Drinfeld A-module of characteristic p0 over a finitely generated field K. Previous articles determined the image of the absolute Galois group of K up to commensurability in its action on all prime-to-p0 torsion points of…

A relationship between nilpotency and primeness in a module is investigated. Reduced modules are expressed as sums of prime modules. It is shown that presence of nilpotent module elements inhibits a module from possessing good structural…

The coincidence of the set of all nilpotent elements of a ring with its prime radical has a module analogue which occurs when the zero submodule satisfies the radical formula. A ring $R$ is 2-primal if the set of all nilpotent elements of…

Let $R$ be a commutative ring with $1$ and $n$ a natural number. We say that a submodule $N$ of $R^n$ is semiprime if for every $f=(f_1,\ldots,f_n) \in R^n$ such that $f_i f \in N$ for $i=1,\ldots,n$ we have $f \in N$. Our main result is…

We generalize results of Alladi, Dawsey, and Sweeting and Woo for Chebotarev densities to general densities of sets of primes. We show that if $K$ is a number field and $S$ is any set of prime ideals with natural density $\delta(S)$ within…

We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…

Let R be a commutative ring with identity and let M be an R-module. The purpose of this paper is to introduce and investigate the submodules of an R-module M which satisfy the dual of Property A, the dual of strong Property A, and the dual…

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…

We investigate rational $G$-modules $M$ for a linear algebraic group $G$ over an algebraically closed field $k$ of characteristic $p > 0$ using filtrations by sub-coalgebras of the coordinate algebra $k[G]$ of $G$. Even in the special case…

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. By $J(R),$ we denote the Jacobson radical of $R$. The purpose of this paper is to introduce the concept of weakly $J$-submodules generalizing $J$-submodules. We…

In this note, we prove two results regarding the variation of K-moduli. The first one reveals the relationship between the chamber decomposition for K-semistable domains and the variation of GIT. The second one presents the relationship…

Let R be a commutative ring with unity, M a module over R and let S be a G-set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form similar to the elements of group ring RG. The…

Let $\phi$ be a Drinfeld $A$-module of finite residual characteristic $\bar{\mathfrak{p}}$ over a local field $K$. We study the action of the inertia group of $K$ on a modified adelic Tate module $\smash{T^\circ_{\text{ad}}}(\phi)$ which…

We fix the lexicographic order $\prec$ on the polynomial ring $S=k[x_{1},...,x_{n}]$ over a ring $k$. We define $\Hi^{\prec\Delta}_{S/k}$, the moduli space of reduced Gr\"obner bases with a given finite standard set $\Delta$, and its open…

In this article, we define the concept of an $S$-$k$-irreducible ideal and $S$-$k$-maximal ideal in a commutative semiring. We also establish several results concerning $S$-$k$-primary ideals and prove the existence theorem and the…

In this paper, we introduce $S$-prime elements in $V$-lattices, where $S$ is a multiplicatively closed subset of a $V$-lattice $L$. In addition, we introduce the $S$-Prime Element Principle to prove that certain elements in $V$-lattices are…

Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…

Let $A$ be a hereditary algebra over an algebraically closed field $k$ and $A^{(m)}$ be the $m$-replicated algebra of $A$. Given an $A^{(m)}$-module $T$, we denote by $\delta (T)$ the number of non isomorphic indecomposable summands of $T$.…

Submodularity is a key property in discrete optimization. Submodularity has been widely used for analyzing the greedy algorithm to give performance bounds and providing insight into the construction of valid inequalities for mixed-integer…