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Criteria for unique factorization in integral domains
Journal article   Open access   Peer reviewed

Criteria for unique factorization in integral domains

D. D Anderson, Scott T Chapman, Franz Halter-Koch and Muhammad Zafrullah
Journal of pure and applied algebra, Vol.127(3), pp.205-218
1998
DOI: 10.1016/S0022-4049(96)00183-1
url
https://doi.org/10.1016/S0022-4049(96)00183-1View
Published (Version of record) Open Access

Abstract

Let R be an integral domain. In this paper, we introduce a sequence of factorization properties which are weaker than the classical UFD criteria. We give several examples of atomic nonfactorial monoids which satisfy these conditions, but show for several classes of integral domains of arithmetical interest that these factorization properties force unique factorization. In particular, we show that if R satisfies any of our properties and is a Krull domain with finite divisor class group, a nonmaximal order in an algebraic number field, or a generalized Cohen-Kaplansky domain, then R in fact must be factorial.

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