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05-02-2021 | Original Paper | Issue 3/2021

Applicable Algebra in Engineering, Communication and Computing 3/2021

Rings whose (proper) cyclic modules have cyclic automorphism-invariant hulls

Journal:
Applicable Algebra in Engineering, Communication and Computing > Issue 3/2021
Authors:
M. Tamer Koşan, Truong Cong Quynh
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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.

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