Let $R$ be a commutative ring and let $M$ be an $R$-module. We define the small intersection graph $G(M)$ of $M$ with all non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M...

In this paper, a single precision IEEE 754 floatingpoint multiplier with high speed and low power is presented. The bottleneck of any single precision floating-point multiplier design is the 24x24 bit integer multiplier. Urdhava Triyakbhyam algorithm of ancient Indian Vedic Mathematics is utilized to improve its efficiency. In the proposed architecture, the 24x24 bit multiplication operation is...

Abstract. We study h-vectors and graded Betti numbers of level modules up to multiplication by a rational number. Assuming a conjecture on the possible graded Betti numbers of Cohen-Macaulaymodules we get a description of the possible h-vectors of level modules up to multiplication by a rational number. We also determine, again up to multiplication by a rational number, the cancellable h-vector...

Let $R\ $be a commutative ring with $1\neq0$ and $M$ be an $R$-module. Suppose that $S\subseteq R\ $is multiplicatively closed set of $R.\ $Recently Sevim et al. in \cite{SenArTeKo} introduced the notion $S$-prime submodule which is generalization prime used them to characterize certain classes rings/modules such as submodules, simple modules, torsion free modules,\ $S$-Noetherian modules etc. ...

let $r$ be a commutative ring and let $m$ be an $r$-module. we define the small intersection graph $g(m)$ of $m$ with all non-small proper submodules of $m$ as vertices and two distinct vertices $n, k$ are adjacent if and only if $ncap k$ is a non-small submodule of $m$. in this article, we investigate the interplay between the graph-theoretic properties of $g(m)$ and algebraic properties of $m...

We study multiplication modules. The rings are not assumed to be commutative. Several criteria with some applications given for a direct sum of modules module.