Factorization in Prüfer Domains

Abstract

We construct a norm on the nonzero elements of a Prüfer domain and extend this concept to the set of ideals of a Prüfer domain. These norms are used to study factorization properties Prüfer of domains.

Hereditary atomicity in integral domains

“…In this final subsection, we offer a potential approach to this question. Much of the material in this subsection is a expository condensation of the last half of the paper [31] and some of the material can be found in [18].…”

Ideal class (semi)groups and atomicity in Prüfer domains

“…We will use the result N (IJ) = N (I) + N (J ). For more on this construction and a proof of the result, see [1].…”

Factorization theory in commutative monoids

“…Various aspects of factorization theory could not be covered in this survey. These include factorizations in non-commutative rings and semigroups ( [86]), factorizations in commutative rings with zero-divisors ( [5]), arithmetic of non-atomic, non-BF, and non-Mori domains ( [8,23,24]), and factorizations into distinguished elements that are not irreducible (e.g., factorizations into radical ideals and others [32,81,75,76]).…”