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Description
| - Kaplansky classes emerged in the context of Enochs' solution of the Flat Cover Conjecture. Their connection to abstract model theory goes back to Baldwin et al.: a class C of roots of Ext is a Kaplansky class closed under direct limits if and only if the pair (C, {=) is an abstract elementary class (AEC) in the sense of Shelah. We prove that this AEC has finite character in case C = C-perpendicular to' for a class C' of pure-injective modules. In particular, all AECs of roots of Ext over any right noetherian right hereditary ring R have finite character (but the case of general rings remains open). If (C, {=) is an AEC of roots of Ext, then C is known to be a covering class. However, Kaplansky classes need not even be precovering in general: We prove that the class D of all aleph(1)-projective modules (which is equal to the class of all flat Mittag-Leffler modules) is a Kaplansky class for any ring R, but it fails to be precovering in case R is not right perfect, the class (perpendicular to)(D-perpendicular to) equals the class of all flat modules and consists of modules of projective dimension {= 1. Assuming the Singular Cardinal Hypothesis, we prove that D is not precovering for each countable non-right perfect ring R.
- Kaplansky classes emerged in the context of Enochs' solution of the Flat Cover Conjecture. Their connection to abstract model theory goes back to Baldwin et al.: a class C of roots of Ext is a Kaplansky class closed under direct limits if and only if the pair (C, {=) is an abstract elementary class (AEC) in the sense of Shelah. We prove that this AEC has finite character in case C = C-perpendicular to' for a class C' of pure-injective modules. In particular, all AECs of roots of Ext over any right noetherian right hereditary ring R have finite character (but the case of general rings remains open). If (C, {=) is an AEC of roots of Ext, then C is known to be a covering class. However, Kaplansky classes need not even be precovering in general: We prove that the class D of all aleph(1)-projective modules (which is equal to the class of all flat Mittag-Leffler modules) is a Kaplansky class for any ring R, but it fails to be precovering in case R is not right perfect, the class (perpendicular to)(D-perpendicular to) equals the class of all flat modules and consists of modules of projective dimension {= 1. Assuming the Singular Cardinal Hypothesis, we prove that D is not precovering for each countable non-right perfect ring R. (en)
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Title
| - Kaplansky classes, finite character and aleph(1)-projectivity
- Kaplansky classes, finite character and aleph(1)-projectivity (en)
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skos:prefLabel
| - Kaplansky classes, finite character and aleph(1)-projectivity
- Kaplansky classes, finite character and aleph(1)-projectivity (en)
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skos:notation
| - RIV/00216208:11320/12:10128138!RIV13-GA0-11320___
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http://linked.open...avai/predkladatel
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA201/09/0816), P(GD201/09/H012), P(MEB101005), Z(MSM0021620839)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/12:10128138
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - aleph1-projectivity; character; finite; classes; Kaplansky (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - DE - Spolková republika Německo
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
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http://linked.open...ain/vavai/riv/wos
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://bibframe.org/vocab/doi
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http://localhost/t...ganizacniJednotka
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is http://linked.open...avai/riv/vysledek
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