Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.

Let R be an associative ring with identity, C(R) be the category of com-plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))−)have enough injectives in C(R). As an application, we prove that for each atcomplex F and each complex Y of R-modules, Exti (F,X)= 0, whenever Ris n-perfect and i > n.

In sub-micron CMOS processes, it has become increasingly difficult to identify and separate outliers from the intrinsic distribution at test. This is due to the increasing inadequacy of reliability screens such as burn-in and IDDQ testing. Statistical Post-Processing (SPP) methods have been developed to run off-tester using the raw data generated from Automatic Test Equipment (ATE) and wafersor...

‎In this paper‎, ‎by using the sequence of multipliers‎, ‎we introduce frames with algebraic bounds in Hilbert pro-$ C^* $-modules‎. ‎We investigate the relations between frames and $ ast $-frames‎. ‎Some properties of $ ast $-frames in Hilbert pro-$ C^* $-modules are studied‎. ‎Also‎, ‎we show that there exist two differences between $ ast $-frames in Hilbert pro-$ C^* $-modules and Hilbert $ ...

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...

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...