The goal of this paper is to give characterizations of minimal primary decompositions and radicals of submodules of any finitely generated module over a PID. To do this, we first consider free modules of finite rank and we characterize prime, primary and maximal submodules as well as minimal primary decompositions and radicals.

By a finite-rank (linear functional) system, we mean a system of linear differential, shift and q-shift operators or, any mixture thereof, whose solution space is finite-dimensional. This poster attempts to develop an algorithm for factoring finite-rank systems into “subsystems” whose solution spaces are of lower dimension. This work consists of three parts: 1. using module-theoretic language t...

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.

let r be a commutative ring with identity and m be a unitary r-module. let : s(m) −! s(m) [ {;} be a function, where s(m) is the set of submodules ofm. suppose n  2 is a positive integer. a proper submodule p of m is called(n − 1, n) − -prime, if whenever a1, . . . , an−1 2 r and x 2 m and a1 . . . an−1x 2p(p), then there exists i 2 {1, . . . , n − 1} such that a1 . . . ai−1ai+1 . . . an−1x...

Let Δ be an abelian group. By considering the notion multiplication of Δ-graded modules (see [7]) over a commutative Δ-graded ring with unity, we introduce the notion of product of two Δ-graded submodules which we use to characterize the Δ-graded prime submodules of a multiplication Δ-graded module. Finally we proved a graded version of Nakayama lemma for multiplication Δ-graded modules.

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...

Roughness in modules have been investigated by B. Davvaz and M. Mahdavipour in 2006 [5]. The purpose of this paper is to introduce and discuss the concept of T -rough prime and primary submodules which is a generalization the lower and upper approximation submodules over a commutative ring. We define a set-valued homomorphism on a module and study some properties of it . We prove some results f...

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...