chapter  23
19 Pages

Integral Morphisms

ByJack Maney

We recall that a domain R is called atomic if every nonzero nonunit can be factored into irreducibles (or atoms). An atomic domain R is called a half-factorial domain, or HFD, if whenever we have a collection of irreducibles {α1, α2, · · · , αm, β1, β2, · · · , βn} with α1 · · ·αm = β1 · · ·βn then n = m.