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Rings whose (proper) cyclic modules have cyclic automorphism-invariant hulls.
- Source :
-
Applicable Algebra in Engineering, Communication & Computing . Jun2021, Vol. 32 Issue 3, p385-397. 13p. - Publication Year :
- 2021
-
Abstract
- The object of this article is associate to automorphism-invariant modules that are invariant under any automorphism of their injective hulls with cyclic modules and cyclic modules have cyclic automorphism-invariant hulls. The study of the first sequence allows us to characterize rings whose cyclic right modules are automorphism-invariant and to show that if R is a right Köthe ring, then R is an Artinian principal left ideal ring in case every cyclic right R-module is automorphism-invariant. The study of the second sequence leads us to consider a generalization of hypercyclic rings that are each cyclic R-module has a cyclic automorphism-invariant hull. Such rings are called right a-hypercyclic rings. It is shown that every right a-hypercyclic ring with Krull dimension is right Artinian. [ABSTRACT FROM AUTHOR]
- Subjects :
- *AUTOMORPHISMS
*ARTIN rings
*GENERALIZATION
Subjects
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 32
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 150472749
- Full Text :
- https://doi.org/10.1007/s00200-021-00494-8