. "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . . "3940" . . . "2014" . "[45F53E07F1AA]" . "15"^^ . . . . . "For any set of modules S, we prove the existence of precovers (right approximations) for all classes of modules of bounded C-resolution dimension, where C is the class of all S-filtered modules. In contrast, we use infinite-dimensional tilting theory to show that the class of all locally free modules induced by a non-Sigma-pure-split tilting module is not precovering. Consequently, the class of all locally Baer modules is not precovering for any countable hereditary artin algebra of infinite representation type."@en . . . . "I, P(GA201/09/0816), S" . "10.1112/blms/bdt069" . "RIV/00216208:11320/14:10285166!RIV15-MSM-11320___" . "For any set of modules S, we prove the existence of precovers (right approximations) for all classes of modules of bounded C-resolution dimension, where C is the class of all S-filtered modules. In contrast, we use infinite-dimensional tilting theory to show that the class of all locally free modules induced by a non-Sigma-pure-split tilting module is not precovering. Consequently, the class of all locally Baer modules is not precovering for any countable hereditary artin algebra of infinite representation type." . "46" . "Approximations and locally free modules"@en . "RIV/00216208:11320/14:10285166" . "Bulletin of the London Mathematical Society" . . . . "Approximations and locally free modules" . . . "Approximations and locally free modules"@en . "covers; cotorsion pairs; compactness theorem"@en . "2"^^ . "000330193400008" . "11320" . "0024-6093" . "Trlifaj, Jan" . "2"^^ . . "Sl\u00E1vik, Alexander" . . "Approximations and locally free modules" . "http://dx.doi.org/10.1112/blms/bdt069" .