A NOTE ON ARTIN-REES NUMBERS

This note focuses on Artin-Rees numbers and the uniformity of such numbers in certain situations. A simple result on principal ideals yields a strong uniformityproperty of Artin-Rees numbers in this case, and also a general expression for anArtin-Rees number in terms of lengths of primary ideals which arise on passage toan appropriate Rees ring. This approach should make Artin-Rees numbers moreamenable to calculation, especially in cases (such as that of complete intersectionideals) where the Rees ring is known in an effective way. We also touch briefly onanalogues for the case of integrally closed ideals. We use [6] as a background reference for the material in this paper. © 1991 Oxford University Press.