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Automorphism-invariant non-singular rings and modules. (English) Zbl 1411.16002
Summary: A ring \(A\) is a right automorphism-invariant right non-singular ring if and only if \(A = S \times T\), where \(S\) a right self-injective regular ring and \(T\) is a strongly regular ring which contains all invertible elements of its maximal right ring of quotients. Over a ring \(A\), each direct sum of automorphism-invariant non-singular right modules is an automorphism-invariant module if and only if the factor ring of the ring \(A\) with respect to its right Goldie radical is a semiprime right Goldie ring.

MSC:
16D50 Injective modules, self-injective associative rings
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
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