Constructing division rings as module-theoretic direct limits

DOI10.1090/S0002-9947-02-02927-6zbMath0995.16014OpenAlexW1554198975MaRDI QIDQ2781399

George M. Bergman

Publication date: 19 March 2002

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-02-02927-6

zbMATH Keywords

endomorphism ringsfree modulesclosure operatorsOre domainsdivision ringsexchange propertydirect limitsfirsdivision rings of fractionscoherent matroidal structuresquotients of localizations

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Endomorphism rings; matrix rings (16S50) Free, projective, and flat modules and ideals in associative algebras (16D40) Automorphisms and endomorphisms (16W20) Infinite-dimensional and general division rings (16K40) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (16E60) Ore rings, multiplicative sets, Ore localization (16U20)

Related Items (3)

Independence algebras, basis algebras and the distributivity condition ⋮ Relatively free algebras with weak exchange properties ⋮ Some results relevant to embeddability of rings (especially group algebras) in division rings

Cites Work

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• Torsion theories, additive semantics, and rings of quotients. With an appendix by H. H. Storrer on torsion theories and dominant dimensions
• Sfields finitely right-generated over subrings
• A Prime Matrix Ideal Yields a Skew Field
• On the Abstract Properties of Linear Dependence
• Embedding Free Algebras in Skew Fields

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