Relatively big projective modules and their applications to direct sum decompositions
Álvarez Arias, Román (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Herbera i Espinal, Dolors (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Prihoda, Pavel (Charles University. Department of Algebra)

Date:	2025
Abstract:	Countably generated projective modules that are relatively big with respect to a trace ideal were introduced by Příhoda, as an extension of Bass' uniformly big projectives. It has already been proved that there are a number of interesting examples of rings whose countably generated projective modules are always relatively big. In this paper, we increase the list of such examples, showing that it includes all right Noetherian rings satisfying a polynomial identity. We also show that countably generated projective modules over locally semiperfect torsion-free algebras over h-local domains are always relatively big. This last result applies to endomorphism rings of finitely generated torsion-free modules over h-local domains. As a consequence, we can give a complete characterization of those h-local domains of Krull dimension 1 for which every direct summand of a direct sum of copies of a single finitely generated torsion-free module is again a direct sum of finitely generated modules.
Grants:	Agencia Estatal de Investigación PID2023-147110NB-I00 Generalitat de Catalunya 2021/SGR-01015
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Direct sum decomposition ; H-local domain ; Monoid ; P.I. ring ; Projective module ; Relatively big projective
Published in:	Journal of algebra and its applications, November 2025, ISSN 1793-6829

DOI: 10.1142/S0219498825420186

Available from: 2026-11-30 Postprint 50 p, 553.1 KB

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