A note on denominator ideals of linear fractional transforms of an anti-integral element over an integral domain
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概要
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Let α be an anti-integral element of degree t over an integral domain R and φα(X) the minimal polynomial of α over the quotient field of R. Let β be a linear fractional transform of α, that is, β=cα-d/aα-b(a, b, c, d∈R, ad-bc∈R*)where R* is the group of units of R. First we describe I[β], the denominator ideal of β, in terms of I[α] and φα(a, b) where φα(X, Y)=Xtφα(Y/X). Next we introduce the ideal ˜{I}[α] concerning integral property of α and α-1. Then we describe ˜{I}[β] by using I[α], φα(a, b) and φα(c, d).
著者
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Yoshida Ken-ichi
Department Of Agrobioscience Graduate School Of Agricultural Science Kobe University
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Baba Kiyoshi
Department Of Math. Faculty Of Education And Welfare Science
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YOSHIDA KEN-ICHI
Department of Applied Mathematics, Okayama University of Science
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SATO Junro
Southern Osaka University
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BABA KIYOSHI
Department of Mathematics, Faculty of Education and Welfare Science, Oita University
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