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


KOŞAN M. T. , Truong Cong Quynh T. C. Q.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol.32, no.3, pp.385-397, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1007/s00200-021-00494-8
  • Journal Name: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.385-397
  • Keywords: Automorphism-invariant module, Automorphism-invariant hull, Cyclic module, Hypercyclic ring, Krull dimension, K&#246, the ring
  • Gazi University Affiliated: Yes

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 Kothe 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.