MODULES CHARACTERIZED BY THEIR SIMPLE SUBMODULES

Rings characterized by their fuzzy submodules

The notions of pure ideals and pure submodules play an important role in the study of rings and their module categories. In this paper, we introduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-module. We establish their basic properties, and use them to obtain fuzzy theoretic characterizations of right weakly regular rings. Among other results, we prove that a ring R is right we...

Weyl Submodules in Restrictions of Simple Modules

Let F be an algebraically closed field of characteristic p > 0. Suppose that SLn−1(F) is naturally embedded into SLn(F) (either in the top left corner or in the bottom right corner). We prove that certain Weyl modules over SLn−1(F) can be embedded into the restriction L(ω)↓SL n−1(F), where L(ω) is a simple SLn(F)-module. This allows us to construct new primitive vectors in L(ω)↓SL n−1(F) from a...

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...

δ-Small Submodules and δ-Supplemented Modules