A Right Countably Sigma-CS Ring with ACC or DCC on Projective Principal Right Ideals is Left Artinian and QF-3

DOI10.2307/2154777zbMath0852.16013OpenAlexW4232459829MaRDI QIDQ4875748

Dinh Van Huynh

Publication date: 8 December 1996

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2154777

zbMATH Keywords

direct sumsdirect summandsquasi-Frobenius ringssemiperfect ringsfinite uniform dimensionCS modulesACC or DCC on projective principal right idealsright countably \(\Sigma\)-CS rings

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Quasi-Frobenius rings (16L60) Noncommutative local and semilocal rings, perfect rings (16L30) Other classes of modules and ideals in associative algebras (16D80) Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) (16P70)

Related Items (12)

On continuous rings ⋮ On indecomposable decompositions of \(CS\)-modules. II ⋮ MODULES SATISFYING EXTENSION CONDITIONS UNDER MONOMORPHISM OF THEIR CLOSED SUBMODULES ⋮ ON A CLASS OF SEMIPERFECT RINGS ⋮ Artinian Rings Characterized by Direct Sums of CS Modules ⋮ WHEN SELF-INJECTIVE RINGS ARE QF: A REPORT ON A PROBLEM ⋮ Some Results on Self-Injective Rings and Σ-CS Rings ⋮ Skew-injective modules ⋮ Modules which are invariant under monomorphisms of their injective hulls ⋮ A note on co-Harada rings ⋮ A note on quasi-Frobenius rings ⋮ Some remarks on CS modules and SI rings

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