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.

本文的目的是与自射不变性模块相关联，这些模块在带有循环模块的内射壳的任何自同构下都是不变的，而循环模块具有循环自同构不变的外壳。对第一个序列的研究使我们能够表征其循环右模块是自同构不变的环，并表明如果R是右Köthe环，则在每个循环右R-模块是自同构的情况下，R是阿蒂尼亚原理的左理想环-不变。对第二个序列的研究使我们考虑了超环环的泛化，每个环的R-模块都具有一个循环自同构不变的外壳。这些环被称为右一-超环。结果表明，每个右旋的具有Krull维数的超环都是正确的Artinian。