NDLI: On precover classes

Content Provider	Springer Nature Link
Author	Bican, Ladislav
Copyright Year	2005
Abstract	SianoG eH classi astratte di moduli. Si dice che la classeH ha laG se per ogni cardinale infinito λ esiste un cardinale κ>λ tale che per ogniF∈H con \|F\|≥κ e ogni suo sottomoduloK con \|F/K\|≤λ esiste un sottomoduloL diK tale cheF/L/teG e \|F/L\|<κ. Questa condizione è più forte della condizione (P) che richiedeL≠0 invece di \|F/L\|<κ, che è stata introdotta e studiata in [8]. In queste note studiamo le relazioni di questa condizione più generale con l'esistenza di prericoprimenti rispetto ad alcune classi di moduli. Come applicazione otteniamo alcune condizioni sufficienti per l'esistenza di prericoprimenti liberi da σ-torsione relativamente ad una data teoria della torsione ereditaria σ per la categoriaR-mod. Questo risultato è strettamente connesso, ed in qualche senso estende, quelli di [5].LetG andH be abstract classes of modules. The classH is said to have theG-property if to each infinite cardinal λ there exists a cardinal κ>λ such that for everyF∈H with \|F\|≥κ and every its submoduleK with \|F/K\|≤λ there exists a submoduleL ofK such thatF/L/teG and \|F/L\|<κ. This condition is stronger than the condition (P) requiringL≠0 instead of \|F/L\|<κ, which was introduced and investigated in [8]. In this note we are going to study the relations of this more general condition to the existence of precovers with respect to some classes of modules. As an application we obtain some sufficient conditions for the existence of σ-torsionfree precovers related to a given hereditary torsion theory σ for the categoryR-mod. This result is closely related to and in some sense extends that of [5].
Starting Page	61
Ending Page	67
Page Count	7
File Format	PDF
ISSN	04303202
Journal	Annali dell’Università di Ferrara
Volume Number	51
Issue Number	1
e-ISSN	18271510
Language	English
Publisher	Springer-Verlag
Publisher Date	2005-01-01
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Precover class hereditary torsion theory injective hull relatively injective hull G-property Module categories, module theory in a category-theoretic context, Morita equivalence and duality Torsion theories; radicals on module categories Torsion theories, radicals Mathematics Analysis Geometry History of Mathematics Numerical Analysis Algebraic Geometry
Content Type	Text
Resource Type	Article
Subject	Mathematics

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