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Description
  • A module M is said to be small if the functor Hom(M,-) commutes with direct sums and right steady rings are exactly those rings whose small modules are necessary finitely generated. We give several results on steadiness of polynomial rings, namely we prove that polynomials over a right perfect ring such that End_R(S) is finitely generated over its center for every simple module S form a right steady ring iff the set of variables is countable. Moreover, every polynomial ring in uncountably many variables is non-steady.
  • A module M is said to be small if the functor Hom(M,-) commutes with direct sums and right steady rings are exactly those rings whose small modules are necessary finitely generated. We give several results on steadiness of polynomial rings, namely we prove that polynomials over a right perfect ring such that End_R(S) is finitely generated over its center for every simple module S form a right steady ring iff the set of variables is countable. Moreover, every polynomial ring in uncountably many variables is non-steady. (en)
Title
  • Steadiness of polynomial rings
  • Steadiness of polynomial rings (en)
skos:prefLabel
  • Steadiness of polynomial rings
  • Steadiness of polynomial rings (en)
skos:notation
  • RIV/00216208:11320/11:10104527!RIV12-MSM-11320___
http://linked.open...avai/predkladatel
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  • Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 2
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  • 232299
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  • RIV/00216208:11320/11:10104527
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  • rings; polynomial; Steadiness (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • UA - Ukrajina
http://linked.open...ontrolniKodProRIV
  • [0C546E850355]
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  • Algebra and Discrete Mathematics
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http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
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  • 2010
http://linked.open...iv/tvurceVysledku
  • Žemlička, Jan
http://linked.open...n/vavai/riv/zamer
issn
  • 1726-3255
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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