In this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over Noetherian rings are proved. More...

Let R be a commutative ring with non-zero identity and let M be a non-zero unitary R-module. The concept of fuzzy coprimary submodule as a dual notion of fuzzy primary one will be introduced and some of its properties will be studied. Among other things, the behavior of this concept with respect to fuzzy localization formation and fuzzy quotient will be examined.

Let R be a commutative ring with identity. Let N and K be two submodules of a multiplication R-module M. Then N=IM and K=JM for some ideals I and J of R. The product of N and K denoted by NK is defined by NK=IJM. In this paper we characterize some particular cases of multiplication modules by using the product of submodules.

This paper designs and implements a hardware-based evolutionary digital filter (EDF). The EDF is an adaptive digital filter which is controlled by adaptive algorithm based on evolutionary computation. The hardware-based EDF consists of two submodules, that is, a filtering and fitness calculation (FFC) module and a reproduction and selection (RS) module. The FFC module has high computational abi...

The decompositions of the Fock and Basic modules of the affine Lie algebra ŝlN into irreducible submodules of the Yangian algebra Y (glN ) are constructed. Each of the irreducible submodules admits the unique up to normalization eigenbasis of the maximal commutative subalgebra of the Yangian. The elements of this eigenbasis are identified with specializations of Macdonald symmetric functions wh...

The modular decomposition of a graph G = (V,E) does not contain prime modules if and only if G is a cograph, that is, if no quadruple of vertices induces a simple connected path P4. The cograph editing problem consists in inserting into and deleting from G a set F of edges so that H = (V,E4F) is a cograph and |F | is minimum. This NP-hard combinatorial optimization 1 ar X iv :1 70 2. 07 49 9v 1...

let $g$ be a group with identity $e$. let $r$ be a $g$-graded commutative ring with a non-zero identity and $m$ be a graded $r$-module. in this article, we introduce the concept of graded almost semiprime submodules. also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.