Rings with an additive rank function

DOI10.1016/0021-8693(90)90280-2zbMath0704.16014OpenAlexW2047220699MaRDI QIDQ916756

Alfred Goldie

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0021-8693(90)90280-2

zbMATH Keywords

reduced rankGabriel filterartinian embeddingmaximal quotient ringright noetherian k- algebraright noetherian ringssimple artinian ringSylvester rank function

Mathematics Subject Classification ID

Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Artinian rings and modules (associative rings and algebras) (16P20) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50) Extensions of associative rings by ideals (16S70)

Cites Work

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• Embeddings in Artinian rings and Sylvester rank functions
• Additive rank functions in Noetherian rings
• Additive rank functions and Gabriel filters in right Noetherian rings
• Quotient rings and localization for Noetherian rings
• Some Pathological Rings of Quotients
• Observations on group rings
• Nil Subrings of Goldie Rings are Nilpotent
• The embedding problem for Noetherian rings

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