let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule 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.  

In this paper we design a system which takes student attendance and the attendance records are maintained automatically in an academic institute. Taking the attendance manually and maintaining its record till end of year (or even beyond) is very difficult job as well as wastage of time and paper. This necessitates an efficient system that would be fully automatic. Top level design of the system...

BACKGROUND The analysis of the potential molecule targets of coronary artery disease (CAD) is critical for understanding the molecular mechanisms of disease. However, studies of global microarray gene co-expression analysis of CAD still remain limited. METHODS Microarray data of CAD (GSE23561) were downloaded from Gene Expression Omnibus, including peripheral blood samples from CAD patients (...

Those of us in the fast-changing field of computing often dismiss anything written more than five years ago as obsolete. Yet several decades-old papers by David L. Parnas [1, 4, 5, 6, 7, 8] are as timely as those published in recent issues of the top journals. Parnas articulates the timeless software design concepts known as information hiding and abstract interfaces. Most programmers would des...

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

BACKGROUND MicroRNAs (miRNAs) are small RNAs that recognize and regulate mRNA target genes. Multiple lines of evidence indicate that they are key regulators of numerous critical functions in development and disease, including cancer. However, defining the place and function of miRNAs in complex regulatory networks is not straightforward. Systems approaches, like the inference of a module networ...

let $r$ be a commutative ring. in this paper we assert some properties of finitely generated comultiplication modules and fitting ideals of them.