Some results relevant to embeddability of rings (especially group algebras) in division rings

DOI10.1016/j.jalgebra.2019.06.021zbMath1489.16015arXiv1812.06123OpenAlexW2905527025WikidataQ127596533 ScholiaQ127596533MaRDI QIDQ2315003

George M. Bergman

Publication date: 31 July 2019

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

Full work available at URL: https://arxiv.org/abs/1812.06123

zbMATH Keywords

coherent matroidal structures on free modulesgroup algebras of right-ordered groupshomomorphisms of rings to division ringsprime matrix ideals

Mathematics Subject Classification ID

Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Infinite-dimensional and general division rings (16K40) Combinatorial aspects of matroids and geometric lattices (05B35) Ordered groups (06F15) Analysis on ordered groups, (H^p)-theory (43A17)

Cites Work

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• An invitation to general algebra and universal constructions.
• Right-ordered groups
• Rational operators of the space of formal series.
• Invertibility of the group ring of a right-ordered group over a skew field
• Determining homomorphisms to skew fields
• Constructing division rings as module-theoretic direct limits
• RATIONAL CLOSURES OF GROUP RINGS OF LEFT-ORDERED GROUPS
• A Prime Matrix Ideal Yields a Skew Field
• Left Ordered Amenable and Locally Indicable Groups
• Coproducts and Some Universal Ring Constructions
• On Ordered Division Rings
• Ordering by Divisibility in Abstract Algebras