Back to Search
Start Over
Prime Submodules and Local Gabriel Correspondence in σ[ M ].
- Source :
-
Communications in Algebra . Jan2012, Vol. 40 Issue 1, p213-232. 20p. - Publication Year :
- 2012
-
Abstract
- We consider the concept of prime submodule defined by Raggi et al. [7]. We find equivalent conditions for a module M progenerator in σ[M], with τ M -Gabriel dimension, to have a one-to-one correspondence between the set of isomorphism classes of indecomposable τ-torsion free injective modules in σ[M] and the set of τ-pure submodules prime in M, where τ is a hereditary torsion theory in σ[M]. Also we give a relation between the concept of prime M-ideal given by Beachy and the concept of prime submodule in M. We obtain that if M is progenerator in σ[M], then these concepts are equivalent. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 40
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 70383907
- Full Text :
- https://doi.org/10.1080/00927872.2010.529095