Rings and modules which are stable under automorphisms of their injective hulls

2013/01/24 by Noyan Er, Er, Noyan, Surjeet Singh +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.RA #msc:16D50 #msc:16U60

paper · pdf · doi:10.48550/arxiv.1301.5841

To appear in Journal of Algebra

arxiv created 2013/01/24 · arxiv updated 2013/01/25

Abstract

It is proved, among other results, that a prime right nonsingular ring (in particular, a simple ring) R is right self-injective if R_R 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.

Related

• Injective and Automorphism-Invariant Non-Singular Modules
• Rings of Invariant Module Type and Automorphism-Invariant Modules
• Automorphism-invariant non-singular rings and modules
• Automorphism-invariant modules
• Rings whose ideals are close to automorphism-invariant