Related papers: Multiplication $(m,n)$-hypermodules

Assuming the Generalized Riemann Hypothesis, we prove the following: If b is an integer greater than one, then the multiplicative order of b modulo N is larger than N^(1-\epsilon) for all N in a density one subset of the integers. If A is a…

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…

In this paper we study recurrences concerning the combinatorial sum $[n,r]_m=\sum_{k\equiv r (mod m)}\binom {n}{k}$ and the alternate sum $\sum_{k\equiv r (mod m)}(-1)^{(k-r)/m}\binom{n}{k}$, where m>0, $n\ge 0$ and r are integers. For…

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 $\text{Red}(M)$ be the sum of all reduced submodules of a module $M$. For modules over commutative rings, $\text{Soc}(M)\subseteq \text{Red}(M)$. By drawing motivation from how $\text{Soc}$-injective modules were defined by Amin et. al.…

We introduce the notion of $\imath$Schur superalgebra, which can be regarded as a type B/C counterpart of the $q$-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed $q$-permutation modules over Hecke…

We consider the deconstruction/reconstruction of extensions in varieties of algebras which are modules expanded by multilinear operators. The parametrization of extensions determined by abelian ideals with unary actions agrees with the…

In the theory of nonlinear partial differential equations we need to explain superposition operators. For modulation spaces equipped with particular ultradifferentiable weights this was done in \cite{rrs}. In this paper we introduce a class…

In 1859, Ernst E. Kummer \cite{erns} introduced the concept prime ideal and after that in 1983 this concept was generalized to prime submodules by R. McCasland \cite{mcca}. In this article, by considering complexes as a generalization of…

Let $\mathcal{M}(n,m;\F \bp^n)$ be the configuration space of $m$-tuples of pairwise distinct points in $\F \bp^n$, that is, the quotient of the set of $m$-tuples of pairwise distinct points in $\F \bp^n$ with respect to the diagonal action…

Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module. For a non-negative integer $n$ it is shown that, if the sets $\Ass_R(\Ext^{n} _{R}(R/I,M))$ and $\Supp_R(\Ext^{i}_{R}(R/I,H^{j}_{I,J} (M)))$ are…

Starting from the notion of $m$-plurisubharmonic function introduced recently by Dieu and studied, in particular, by Harvey and Lawson, we consider $m$-(semi-)positive $(1,\,1)$-currents and Hermitian holomorphic line bundles on complex…

A locally integrable function $m(\xi,\eta)$ defined on $\mathbb R^n\times \mathbb R^n$ is said to be a bilinear multiplier on $\mathbb R^n$ of type $(p_1,p_2, p_3)$ if $$ B_m(f,g)(x)=\int_{\mathbb R^n} \int_{\mathbb R^n}\hat f(\xi)\hat…

In that paper, we recall the notion of the multidegree for $D$-modules, as exposed in a previous paper, with a slight simplification. A particular emphasis is given on hypergeometric systems, used to provide interesting and computable…

We give a survey of a variety of recent results about the distribution and some geometric properties of points $(x,y)$ on modular hyperbolas $xy \equiv a \pmod m$. We also outline a very diverse range of applications of such results,…

Let S be an m-system of a ring R, and P a submodule of a right R-module M. This paper, presents the notion of S-prime submodule and provides some properties and equivalent definitions. We define S-multiplication right module, and prove that…

In this paper we aim to introduce some hyperideals such as q-primary, (k,n)-absorbing q-primary, sq-primary, wsq-primary hyperideals.

The addition-deletion theorems for hyperplane arrangements, which were originally shown in [H. Terao, Arrangements of hyperplanes and their freeness I, II. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), 293--320], provide useful ways to…

Multiplicative Hitchin systems are analogues of Hitchin's integrable system based on moduli spaces of G-Higgs bundles on a curve C where the Higgs field is group-valued, rather than Lie algebra valued. We discuss the relationship between…

A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom_R(C,C) \cong R and Ext^i_R(C,C) = 0 for all i \geq 1. For certain local Cohen-Macaulay rings (R,m), we verify the equality of Hilbert-Samuel…