Projective modules are determined by their radical factors.

DOI10.1016/j.jpaa.2006.12.004zbMath1124.16002OpenAlexW2138351972WikidataQ105315494 ScholiaQ105315494MaRDI QIDQ886270

Pavel Příhoda

Publication date: 26 June 2007

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2006.12.004

zbMATH Keywords

Jacobson radicalindecomposable projective modulessemilocal ringsinfinitely generated projective modules

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) Noncommutative local and semilocal rings, perfect rings (16L30)

Related Items

Pure projective modules over chain domains with Krull dimension ⋮ Reconstructing projective modules from its trace ideal. ⋮ CLASSIFYING PROJECTIVE MODULES OVER SOME SEMILOCAL RINGS ⋮ Structure of \(H\)-semiprime Artinian algebras. ⋮ Pure projective modules over exceptional uniserial noncoherent rings. ⋮ Classifying Modules in Add of a Class of Modules with Semilocal Endomorphism Rings ⋮ Projective modules over the Gerasimov-Sakhaev counterexample. ⋮ Generalizations of projectivity and supplements revisited for superfluous ideals ⋮ Infinitely generated projective modules over pullbacks of rings ⋮ Direct-sum decompositions of modules with semilocal endomorphism rings ⋮ Fair-sized projective modules. ⋮ An indecomposable direct summand of a serial module which is not uniserial ⋮ Big projective modules over noetherian semilocal rings

Cites Work

• Unnamed Item
• Unnamed Item
• A counterexample to two hypotheses on projective and flat modules
• Liberte des gros modules projectifs
• Projective modules over non-commutative semilocal rings
• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• Projective modules over the endomorphism ring of a biuniform module.
• \(K_0\) of a semilocal ring
• Supplement to 'Projective modules over weakly noetherian ring'
• Flat modules and lifting of finitely generated projective modules.
• On uniserial modules that are not quasi-small.
• Projective and free modules
• Modules with decompositions that complement direct summands
• Projective modules over weakly noetherian rings
• Big projective modules are free
• SOME MODEL THEORY OVER AN EXCEPTIONAL UNISERIAL RING AND DECOMPOSITIONS OF SERIAL MODULES
• Projective Modules
• A Version of the Weak Krull–Schmidt Theorem for Infinite Direct Sums of Uniserial Modules
• Some model theory over a nearly simple uniserial domain and decompositions of serial modules