Automorphism-invariant modules. (English. Russian original) Zbl 1331.16002
J. Math. Sci., New York 206, No. 6, 694-698 (2015); translation from Fundam. Prikl. Mat. 18, No. 4, 129-135 (2013).
In this paper, the author studies automorphism-invariant modules. He proves that for a ring \(A\), every nonsingular, automorphism-invariant right \(A\)-module is injective if and only if the factor ring \(A/G(A_A)\) is right strongly semiprime where \(G(A_A)\) is the right Goldie radical of the ring \(A\). This result is an improvement of the result of Kutami and Oshiro. He also proves that if \(A\) is a prime ring then every nonsingular, automorphism-invariant right \(A\)-module is quasi-injective. This is an improvement of a result of Er, Singh and Srivastava. To prove these two results, the author derives some properties of a nonsingular, square-free, automorphism-invariant right \(A\)-module for a ring \(A\).
Reviewer: Veereshwar A. Hiremath (Dharwad)
MSC:
| 16D50 | Injective modules, self-injective associative rings |
| 16W20 | Automorphisms and endomorphisms |
| 16N60 | Prime and semiprime associative rings |
Keywords:
automorphism-invariant modules; nonsingular modules; Goldie radical; strongly semiprime rings; quasi-injective modulesReferences:
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