Weak Normality and Strong t-closedness of Generalized Power Series Rings

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 3,  2008, pp.443-455
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.3.443
Title & Authors
Weak Normality and Strong t-closedness of Generalized Power Series Rings
Kim, Hwan-Koo; Kwon, Eun-Ok; Kwon, Tae-In;

Abstract
For an extension $\small{A\;{\subseteq}\;B}$ of commutative rings, we present a sufficient conditio for the ring $\small{[[A^{S,\;\leq}]]}$ of generalized power series to be weakly normal (resp., stronglyt-closed) in $\small{[[B^{S,\;\leq}]]}$, where (S, $\small{\leq}$) be a torsion-free cancellative strictly ordered monoid. As a corollary, it can be applied to the ring of power series in infinitely many indeterminates as well as in finite indeterminates.
Keywords
weak normality;(strong) t-closedness;generalized power seriesring;
Language
English
Cited by
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