Rings and modules which are stable under automorphisms of their injective hulls
By Noyan Er, Surjeet Singh, Ashish Kumar Srivastava. 2013
78 citations recorded by the source corpus.
It is proved, among other results, that a prime right nonsingular ring (in particular, a simple ring) R is right self-injective if RR is invariant under automorphisms of its injective hull. This answers two questions raised by Singh and Srivastava, and Clark and Huynh. An example is given to show that this conclusion no longer holds when prime ring is replaced by semiprime ring in the above assumption. Also shown is that automorphism-invariant modules are precisely pseudo-injective modules, answering a recent question of Lee and Zhou. Furthermore, rings whose cyclic modules are automorphism-invariant are investigated.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a3d362d1c59ac78893f92a29bf9ea9fea048b9f0
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Automorphism-invariant modules satisfy the exchange property (2013, background): “As M is automorphism-invariant, this means that the monomorphism h|N : N → L ⊆ M extends to an endomorphism t :M →M (see [5]).”