In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

Our new meeting room, the MR Square, was built as a testing ground of a variety of multimedia user interfaces and applications. The MR Square features mixed-reality technologies such as wide-area trackers and tens of head mount displays, as well as one 200-inch and two 150-inch screens. Participants sit and collaborate in fully wired, retractable seats. The MR Square illustrates how state of th...

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...

Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $mbox{Max}$-injective and $mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and strongly top modules to these classes of modules and obtain some related results.

‎We introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎We also introduce the concept of $(I,J)$-Cohen--Macaulay modules as a generalization of concept of Cohen--Macaulay modules‎. ‎These kind of modules are different from Cohen--Macaulay modules‎, as an example shows‎. ‎Also an art...

in this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.