Superficial sets of elements for sets of ideals

摘要

Leti1,#x2026;,igH1#x2026;,Hf(g#x2265;1,f#x2265;1) be ideal in a a Noetherian ring R,letj1#x2026;,jgbe poitiveintegers,and let be an element in Ij1i(i=1,#x2026;,g). then b1#x2026;,bgare a superficial set of element of degree j1#x2026;,jgforI1#x2026;,Ig; H11#x2026;,hfin case there exist positve interers c1#x2026;,cgsuch thatforH=1#x2026;,for allki#x2265;ciand for all ni#x2265;0(i=1,#x2026;,g) In this paper we show the existence of such sets of elements, characterize them in sevaral ways(when eitherf=1 and H1=R Or Rad(I1#x2026;I1)#x2286;Rad(H1#x2026;,Hh)), show a few of their basic properties and use them to show that if each Iiis regular then for all ideals H in R,for all large kiand for allni#x2265;(i=1,#x2026;,g)