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Algebra Discrete Math., 2010, Volume 10, Issue 2, Pages 107–117 (Mi adm52)  

RESEARCH ARTICLE

Steadiness of polynomial rings

J. Žemlička

Department of Algebra, Charles University in Prague, Faculty of Mathematics and Physics Sokolovská 83, 186 75 Praha 8, Czech Republic

Abstract: 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 $\it{End}_R(S)$ 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.

Keywords: small module, steady ring, polynomial ring.

Full text: PDF file (240 kB)

Bibliographic databases:
MSC: 16S36, 16D10
Received: 10.04.2009
Revised: 03.03.2011
Language:

Citation: J. Žemlička, “Steadiness of polynomial rings”, Algebra Discrete Math., 10:2 (2010), 107–117

Citation in format AMSBIB
\Bibitem{Zem10}
\by J.~{\v Z}emli{\v{c}}ka
\paper Steadiness of polynomial rings
\jour Algebra Discrete Math.
\yr 2010
\vol 10
\issue 2
\pages 107--117
\mathnet{http://mi.mathnet.ru/adm52}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2884747}
\zmath{https://zbmath.org/?q=an:1212.16052}


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