Journal article
Modules whose quotients have finite Goldie dimension
Pacific journal of mathematics, Vol.69(2), pp.337-338
04/01/1977
DOI: 10.2140/pjm.1977.69.337
Abstract
If M is a module and M is a submodule of M, then N is irreducible in M if N cannot be written as a proper intersection of two submodules of M. The purpose of this note is to study modules whose submodules can be written as a finite intersection of irreducible submodules. Such modules are characterized by the fact that their quotients all have finite Goldie dimension, so they are called q.f.d. modules. The main result is: A module M is q.f.d. if and only if every submodule N has a finitely generated submodule T such that N/T has no maximal submodules. Because T is finitely generated this generalizes a theorem of Shock (using his ideas), who showed a q.f.d. module M having the property that every subquotient of M has a maximal submodule must be noetherian (and conversely, of course). © 1977 Pacific Journal of Mathematics. All rights reserved.
Details
- Title: Subtitle
- Modules whose quotients have finite Goldie dimension
- Creators
- Victor Camillo
- Resource Type
- Journal article
- Publication Details
- Pacific journal of mathematics, Vol.69(2), pp.337-338
- DOI
- 10.2140/pjm.1977.69.337
- ISSN
- 0030-8730
- eISSN
- 1945-5844
- Language
- English
- Date published
- 04/01/1977
- Academic Unit
- Mathematics
- Record Identifier
- 9984241051502771
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