On dual pairs and simple-injective modules

DOI10.1006/jabr.1999.8159zbMath0953.16005OpenAlexW1998827941WikidataQ122587065 ScholiaQ122587065MaRDI QIDQ1974170

Mari Morimoto, Takeshi Sumioka

Publication date: 21 January 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8159

zbMATH Keywords

bimodulesdual ringslinearly compact modulesannihilatorsfinitely generated right modulesdual pairssemiperfect ringsGoldie dimensionsquasi-dual modulesright quasi-dual ringssimple-injectivity

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Noncommutative local and semilocal rings, perfect rings (16L30) Bimodules in associative algebras (16D20) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Cites Work

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• Character modules, submodules of a free module, and quasi-Frobenius rings
• On dual rings and their modules
• Rings with Morita duality
• On dual-bimodules
• Injective pairs in perfect rings
• Mininjective rings
• Generalizations of theorems of Fuller
• Note on almost relative projectives and almost relative injectives
• Colocal pairs in perfect rings
• A generalization of quasi-Frobenius rings
• On indecomposable injectives over artinian rings
• Duality theorem of character modules for rings with minimum condition
• Modules with decompositions that complement direct summands
• On perfect simple-injective rings
• On a theorem of Fuller

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