Direct-sum representations of injective modules

DOI10.1016/0021-8693(67)90035-XzbMath0173.03203WikidataQ123190160 ScholiaQ123190160MaRDI QIDQ2531882

Carl Faith, Elbert A. Walker

Publication date: 1967

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

associative rings

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finiteness of the injective hull
• Injective modules over Noetherian rings
• Projective modules
• Relative homological algebra and Abelian groups
• Lectures on injective modules and quotient rings
• Rings for which every module is a direct sum of cyclic modules
• Über injektive Moduln
• On the Dimension of Modules and Algebras, II: (Frobenius Algebras and Quasi-Frobenius Rings)
• Semi-Prime Rings with Maximum Condition
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Direct Products of Modules
• Rings with Ascending Condition on Annihilators
• Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem
• Solution of a Problem of G. Koethe
• On injective modules

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