Abstract
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 considered. We also give two descriptions for the trace of a pure submodule of a multiplication module.
| Original language | English |
|---|---|
| Pages (from-to) | 61-74 |
| Number of pages | 14 |
| Journal | Beitrage zur Algebra und Geometrie |
| Volume | 45 |
| Issue number | 1 |
| Publication status | Published - 2004 |
Keywords
- Flat module
- Idempotent submodule
- Multiplication module
- Projective module
- Pure submodule
- Radical of a module
- Trace of a module
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology