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  • The structure of almost projective modules can be better understood in the case when the following Condition (P) holds: The union of each countable pure chain of projective modules is projective. We prove this condition, and its generalization to pure-projective modules, for all countable rings, using the new notion of a strong submodule of the union. However, we also show that Condition (P) fails for all Prüfer domains of finite character with uncountable spectrum, and in particular, for the polynomial ring KTxU, where K is an uncountable field. One can even prescribe the 0-invariant of the union. Our results generalize earlier work of Hill,and complement recent papers by Macías-Díaz, Fuchs, and Rangaswamy.
  • The structure of almost projective modules can be better understood in the case when the following Condition (P) holds: The union of each countable pure chain of projective modules is projective. We prove this condition, and its generalization to pure-projective modules, for all countable rings, using the new notion of a strong submodule of the union. However, we also show that Condition (P) fails for all Prüfer domains of finite character with uncountable spectrum, and in particular, for the polynomial ring KTxU, where K is an uncountable field. One can even prescribe the 0-invariant of the union. Our results generalize earlier work of Hill,and complement recent papers by Macías-Díaz, Fuchs, and Rangaswamy. (en)
Title
  • Strong submodules of almost projective modules
  • Strong submodules of almost projective modules (en)
skos:prefLabel
  • Strong submodules of almost projective modules
  • Strong submodules of almost projective modules (en)
skos:notation
  • RIV/00216208:11320/11:10107682!RIV12-GA0-11320___
http://linked.open...avai/predkladatel
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/09/0816), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 232701
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/11:10107682
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • modules; projective; almost; submodules; Strong (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [0FE6C7387CC6]
http://linked.open...i/riv/nazevZdroje
  • Pacific Journal of Mathematics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 254
http://linked.open...iv/tvurceVysledku
  • Trlifaj, Jan
  • Braun, Gábor
http://linked.open...n/vavai/riv/zamer
issn
  • 0030-8730
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
is http://linked.open...avai/riv/vysledek of
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