The purpose of this paper is to study the structure of rings over which every essential extension of a direct sum of a family of simple modules is a direct… Click to show full abstract
The purpose of this paper is to study the structure of rings over which every essential extension of a direct sum of a family of simple modules is a direct sum of automorphism-invariant modules. We show that if [Formula: see text] is a right quotient finite dimensional (q.f.d.) ring satisfying this property, then [Formula: see text] is right Noetherian. Also, we show a von Neumann regular (semiregular) ring [Formula: see text] with this property is Noetherian. Moreover, we prove that a commutative ring with this property is an Artinian principal ideal ring.
Keywords:
direct sum;
sum automorphism;
invariant modules;
automorphism invariant
Journal Title: Journal of Algebra and Its Applications
Year Published: 2019
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Journal Title: Journal of Algebra and Its Applications
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!