SOME EXAMPLES OF ALMOST GCD-DOMAINS

Abstract

Let D be an integral domain, X be an indeterminate over D, and D[X] be the polynomial ring over D. We show that D is an almost weakly factorial PvMD if and only if D + XDS[X] is an integrally closed almost GCD-domain for each (saturated) multiplicative subset S of D, if and only if D + XD1[X] is an integrally closed almost GCD-domain for any t-linked overring D1 of D, if and only if D1 + XD2[X] is an integrally closed almost GCD-domain for all t-linked overrings D1 ⊆ D2 of D.

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