Abstract
Let D be an integral domain, D be the integral closure of D, and 0 be a numerical semigroup with0 ( N0. 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.fa g/ of D, there exists a positive integer nD n.fa g/ such that.fa n g/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 D is a bounded root extension, then D is an AK-domain (resp., AUFdomain) if and only if D is a Krull domain (resp., Krull domain with torsion t-class group) and D is t-linked under D. We also prove that if D is a Krull domain (resp., UFD) with char. D/6D0, then the (numerical) semigroup ring DT0U is a nonintegrally closed AK-domain (resp., AUF-domain).
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