Weak diamond, weak projectivity, and transfinite extensions of simple artinian rings

DOI10.1016/j.jalgebra.2022.03.009OpenAlexW4220700706MaRDI QIDQ2122214

Jan Trlifaj

Publication date: 6 April 2022

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

Full work available at URL: https://arxiv.org/abs/2203.06005

zbMATH Keywords

von Neumann regular ringsemiartinian ringweak diamond principleweakly projective module

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Projectives and injectives (category-theoretic aspects) (18G05) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Cites Work

• Approximations and endomorphism algebras of modules. Volume 1: Approximations. Volume 2: Predictions.
• On Whitehead modules
• Test sets for factorization properties of modules
• The dual Baer criterion for non-perfect rings
• When \(R\) is a testing module for projectivity?
• Dually slender modules and steady rings
• Faith’s problem on $R$-projectivity is undecidable
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item