All rings are commutative with 1 6= 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an R-module M is called a 2-absorbing primary submodule of M if whenever a, b ∈ R and m ∈M and abm ∈ N , then am ∈M -rad(N) or bm ∈M -rad(N) or ...

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory  on  Hilbert $C^*$-modules is studied.

in this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von neumann's regular rings. furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

in this paper we introduce a generalization of m-small modules and discuss about the torsion theory cogenerated by this kind of modules in category . we will use the structure of the radical of a module in  and get some suitable results about this class of modules. also the relation between injective hull in  and this kind of modules will be investigated in this article.   for a module  we show...

in this paper, we considered composition operators on weighted hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a hilbert-schmidt characterization and characterizes the membership in schatten-class for these operators. also, closed range composition operators  are investigated.

Each matrix representation : G ?! GL n (K) of a nite group G over a eld K induces an action of G on the module A n over the polynomial algebra A = Kx 1 ; ; x n ]. The graded A-submodule M() of A n generated by the orbit of (x 1 ; ; x n) is studied. A decomposition of M() into generic modules is given. Relations between the numerical invariants of and those of M(), the later being eeciently comp...

In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators  are investigated.

Each matrix representation P: G —> GLn(K) of a finite Group G over a field K induces an action of G on the module A over the polynomial algebra A = K [ x 1 , . . . , xn]. The graded A-submodule M(P) of A generated by the orbit of (x1, ..., xn) is studied. A decomposition of MO) into generic modules is given. Relations between the numerical invariants of P and those of M(P), the latter being eff...

let $m$ be a module over a commutative ring $r$ and let $n$ be a proper submodule of $m$. the total graph of $m$ over $r$ with respect to $n$, denoted by $t(gamma_{n}(m))$, have been introduced and studied in [2]. in this paper, a generalization of the total graph $t(gamma_{n}(m))$, denoted by $t(gamma_{n,i}(m))$ is presented, where $i$ is an ideal of $r$. it is the graph with all elements of $...

A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established. Applications are given to the metric structure of graded ideals in C[z1, . . . , zd], and the existence of “inner” sequences for closed submodules of the free Hilbert module H(C).