• Title/Summary/Keyword: t-rational extensions

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ON MAXIMAL PRERADICAL RATIONAL EXTENSIONS

  • Cho, Yong-Uk
    • East Asian mathematical journal
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    • v.19 no.2
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    • pp.251-259
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    • 2003
  • The concepts of t-rational extensions and t-essential extensions of modules, where t a preradical for R-Mod, are introduced. The structures of such extensions are determined. Relations between maximal t-rational extensions and other concepts of modules are studied.

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ℓ-RANKS OF CLASS GROUPS OF FUNCTION FIELDS

  • Bae, Sung-Han;Jung, Hwan-Yup
    • Journal of the Korean Mathematical Society
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    • v.49 no.1
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    • pp.49-67
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    • 2012
  • In this paper we give asymptotic formulas for the number of ${\ell}$-cyclic extensions of the rational function field $k=\mathbb{F}_q(T)$ with prescribe ${\ell}$-class numbers inside some cyclotomic function fields, and density results for ${\ell}$-cyclic extensions of k with certain properties on the ideal class groups.