Finite factorization domains

Anderson, D.; Mullins, Bernadette

doi:10.1090/S0002-9939-96-03284-4

Finite factorization domains
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by D. D. Anderson and Bernadette Mullins PDF

Proc. Amer. Math. Soc. 124 (1996), 389-396 Request permission

Abstract:

An integral domain $R$ is a finite factorization domain if each nonzero element of $R$ has only finitely many divisors, up to associates. We show that a Noetherian domain $R$ is an FFD $\Leftrightarrow$ for each overring $R’$ of $R$ that is a finitely generated $R$-module, $U(R’)/U(R)$ is finite. For $R$ local this is also equivalent to each $R/[R:R’]$ being finite. We show that a one-dimensional local domain $(R,M)$ is an FFD $\Leftrightarrow$ either $R/M$ is finite or $R$ is a DVR.

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