The notion of simple-direct-injective modules which are a generalization injective unifies $C2$ and $C3$-modules. In the present paper, we introduce semisimple-direct-injective module gives unified viewpoint $C2$, $C3$, SSP properties modules. It is proved that ring $R$ Artinian serial with Jacobson radical square zero if only every right $R$-module has and, for any family simple $R$-modules $\...

Let (X,⟨⋅,⋅⟩) be a Hilbert C∗-module over C∗-algebra A and let S(A) the set of states on A. In this paper, we first compute norm derivative for nonzero elements x y X as follows: limt→0+‖x+ty‖−‖x‖t=1‖x‖max{Reφ(⟨x,y⟩):φ∈S(A),φ(⟨x,x⟩)=‖x‖2}.We then apply it to characterize different concepts orthogonality in X. particular, present simpler proof classical characterization Birkhoff–James C∗-modules...

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 ...

According to most Evolutionary Psychologists, human moral attitudes are rooted in cognitive modules that evolved in the Stone Age to solve problems of social interaction. A crucial component of their view is that such cognitive modules remain unchanged since the Stone Age, and I question that here. I appeal to evolutionary rollback, the phenomenon where an organ becomes non-functional and event...

We study reflexive modules over one dimensional Cohen-Macaulay rings. Our key technique exploits the concept of I I -Ulrich modules.

‎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 $c_2=0$.

Let M be a module over an associative ring R and σ[M ] the category of M -subgenerated modules. Generalizing the notion of a projective generator in σ[M ], a module P ∈ σ[M ] is called tilting in σ[M ] if (i) P is projective in the category of P -generated modules, (ii) every P -generated module is P presented, and (iii) σ[P ] = σ[M ]. We call P self-tilting if it is tilting in σ[P ]. Examples ...

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...