let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

In this paper we see how the module structure of Algebra plays a vital role in coding theory in different branches of Engineering mainly in Information Technology, Electronics and Telecommunications Engineering, Computer Science etc. The basic result was given by S. K. Sarkar [1] for group code. Here I generalize this concept for module theory in algebra and I introduce the concept module code....

we first characterize $tau$-complemented modules with relative (pre)-covers. we also introduce an extending module relative to $tau$-pure submodules on a hereditary torsion theory $tau$ and give its relationship with $tau$-complemented modules.

Recent syntactic theory has aimed for a theory of grammar rich enough to be descriptively adequate, but restricted enough to make plausible claims about the acquisition of 3such systems. Thus in Chomsky's trace theory, sentences, their constituent structures and grammatical relations are determined by a few simple rules which in themselves would generate many non-sentences, but which are constr...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

Rough set theory is a generalisation of classical set theory. It is an effective mathematical approach to deal with vagueness and ambiguity in information systems. Combining this theory with rough algebraic structures is a recent trend in the area of mathematical research. In this paper we consider G -module as the universal set and we introduce the notion of rough G -module with respect to a G...