Dual automorphism-invariant modules over perfect rings

DOI10.1134/S0037446617050019zbMath1381.16040OpenAlexW2766451046MaRDI QIDQ1694699

A. N. Abyzov, Truong Cong Quynh, Dinh Duc Tai

Publication date: 6 February 2018

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446617050019

zbMATH Keywords

perfect ringdual automorphism-invariant moduleHopf modulepseudoprojective module

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Injective modules, self-injective associative rings (16D50) Automorphisms and endomorphisms (16W20) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70)

Related Items (9)

Unnamed Item ⋮ Modules coinvariant under the idempotent endomorphisms of their covers ⋮ On (weakly) co-Hopfian automorphism-invariant modules ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Extending and lifting of endomorphisms and automorphisms of modules over non-primitive HNP rings ⋮ Modules that are invariant with respect to automorphisms and idempotent endomorphisms of their hulls and covers ⋮ Decompositions of dual automorphism invariant modules over semiperfect rings ⋮ Modules which are invariant under nilpotents of their envelopes and covers

Cites Work

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• Automorphism-extendable modules.
• Continuous modules are clean.
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• Hopfian rings and Hopfian modules
• Dual generalizations of the Artinian and Noetherian conditions
• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• Generalized Hopfian modules
• Dual automorphism-invariant modules.
• Automorphism-invariant modules satisfy the exchange property.
• Bezout modules and rings.
• Automorphism-invariant semi-Artinian modules
• Surjective endomorphisms of finitely generated modules

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