Automorphism-invariant non-singular rings and modules

2017/01/25 by Tuganbaev, Askar
#16D #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1701.07116

Abstract

Theorem 1.2. For a ring A, the following conditions are equivalent. 1) A is a right automorphism-invariant right non-singular ring. 2) A is a right automorphism-invariant regular ring. 3) A=S× T, where S is a right injective regular ring and T is a strongly regular ring which contains all invertible elements of its maximal right ring of quotients. Theorem 1.5. For a ring A with right Goldie radical G(A_A), the following conditions are equivalent. 1) A/G(A_A) is a semiprime right Goldie ring. 2) Any direct sum of automorphism-invariant non-singular right A-modules is an automorphism-invariant module. 3) Any direct sum of automorphism-invariant non-singular right A-modules is an injective module.

Related

• Injective and Automorphism-Invariant Non-Singular Modules
• Modules over strongly semiprime ring
• Rings and modules which are stable under automorphisms of their injective hulls
• Rings of Invariant Module Type and Automorphism-Invariant Modules
• Rings whose ideals are close to automorphism-invariant