Submodules of secondary modules

Submodules of Secondary Modules

Pure Submodules of Multiplication Modules

The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...

The secondary radicals of submodules

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper, we will introduce the secondary radical of a submodule $N$ of $M$ as the sum of all secondary submodules of $M$ contained in $N$, denoted by $sec^*(N)$, and explore the related properties. We will show that this class of modules contains the family of second radicals properly and can be regarded as a dual o...

On the Prime Submodules of Multiplication Modules

By considering the notion of multiplication modules over a commutative ring with identity, first we introduce the notion product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module. Finally, we state and prove a version of Nakayama lemma for multiplication modules and find some related basic results. 1. Introduction. Let R b...

Submodules of Specht Modules for Weyl Groups

The construction of all irreducible modules of the symmetric groups over an arbitrary field which reduce to Specht modules in the case of fields of characteristic zero is given by G.D.James. Halıcıoğlu and Morris describe a possible extension of James’ work for Weyl groups in general, where Young tableaux are interpreted in terms of root systems. In this paper we show how to construct submodule...