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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F11%3A10104527%21RIV12-MSM-11320___
rdf:type
n3:Vysledek skos:Concept
dcterms: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.
dcterms:title
Steadiness of polynomial rings Steadiness of polynomial rings
skos:prefLabel
Steadiness of polynomial rings Steadiness of polynomial rings
skos:notation
RIV/00216208:11320/11:10104527!RIV12-MSM-11320___
n3:predkladatel
n4:orjk%3A11320
n5:aktivita
n6:Z
n5:aktivity
Z(MSM0021620839)
n5:cisloPeriodika
2
n5:dodaniDat
n10:2012
n5:domaciTvurceVysledku
n18:5068592
n5:druhVysledku
n14:J
n5:duvernostUdaju
n7:S
n5:entitaPredkladatele
n9:predkladatel
n5:idSjednocenehoVysledku
232299
n5:idVysledku
RIV/00216208:11320/11:10104527
n5:jazykVysledku
n12:eng
n5:klicovaSlova
rings; polynomial; Steadiness
n5:klicoveSlovo
n11:polynomial n11:rings n11:Steadiness
n5:kodStatuVydavatele
UA - Ukrajina
n5:kontrolniKodProRIV
[0C546E850355]
n5:nazevZdroje
Algebra and Discrete Mathematics
n5:obor
n15:BA
n5:pocetDomacichTvurcuVysledku
1
n5:pocetTvurcuVysledku
1
n5:rokUplatneniVysledku
n10:2011
n5:svazekPeriodika
2010
n5:tvurceVysledku
Žemlička, Jan
n5:zamer
n16:MSM0021620839
s:issn
1726-3255
s:numberOfPages
11
n19:organizacniJednotka
11320