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ISSN : 1226-0657

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Vol.4 No.1

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1997, v.4 no.1, pp.93-96
Oh, Heung-Joon
Oh,, H. (1997). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 4(1), 93-96.

Abstract

An atomic integral domain R is a half-factorial domain (HFD) if whenever <TEX>$\chi_1$</TEX>… <TEX>$\chi_{m}=y_1$</TEX>…<TEX>$y_n$</TEX> with each <TEX>$\chi_{i},y_j \in R$<TEX> irreducible, then m = n. In this paper, we show that if R[X] is an HFD, then <TEX>$Cl_{t}(R)$</TEX> <TEX>$\cong$</TEX> <TEX>$Cl_{t}$</TEX>(R[X]), and if <TEX>$G_1$</TEX> and <TEX>$G_2$</TEX> are torsion abelian groups, then there exists a Dedekind HFD R such that Cl(R) = <TEX>$G_1\bigoplus\; G_2$</TEX>.

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half-factorial domain

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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