ALMOST FACTORIALITY OF INTEGRAL DOMAINS AND KRULL-LIKE DOMAINS

作者:Chang Gyu Whan*; Kim Hwankoo; Lim Jung Wook
来源:Pacific Journal of Mathematics, 2012, 260(1): 129-148.
DOI:10.2140/pjm.2012.260.129

摘要

Let D be an integral domain, (D) over bar be the integral closure of D, and Gamma be a numerical semigroup with Gamma subset of N-0. Let t be the so-called t-operation on D. We will say that D is an AK-domain (resp., AUF-domain) if for each nonzero ideal. ({a(alpha)}) of D, there exists a positive integer n = n({a(alpha)})such that ({a(alpha)(n)})(t) is t-invertible (resp., principal). In this paper, we study several properties of AK-domains and AUF-domains. Among other things, we show that if D subset of (D) over bar is a bounded root extension, then D is an AK-domain (resp., AUF-domain) if and only if (D) over bar is a Krull domain (resp., Krull domain with torsion t-class group) and (D) over bar is t-linked under (D) over bar. We also prove that if D is a Krull domain (resp., UFD) with char. (D) not equal 0, then the (numerical) semigroup ring D[Gamma] is a nonintegrally closed AK-domain (resp., AUF-domain).

  • 出版日期2012-11

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