Über superfizielle Systeme von Parametern

Abstract

in Rost'ock (Eingegangen am 17. 12. 1976) 0. (R, M ) sei ein lokaler Ring mit der KRuLL-Dimension d (d 2 1) und dem maximalen Ideal M . Q G M sei ein eigentliches Ideal in R. In [2], Theorem 3, beweist D. KIRBY, da13 ein Element ~€ 9 " (s t 1) genau dann superfiziell vom Grad s ist, wenn fur hinreichend grol3e n die Beziehung (~) n Q ' +~= ( x )

Absolutely superficial sequences

“…(2) A.s. sequences are closely related with other specified sequences of (4), (6), (11), (15). A natural consequence of this fact is the characterization of generalized Cohen-Macaulay (resp.…”

“…(2) A superficial element of a for M is an element be a for which there exist integers c > 0, d > 0 such that (a n+c M:b) n a d M = a n M for all sufficiently large n. Thus, we call a 1 ,..., a T an a-superficial M-sequence if a i is a superficial element of q for M/q^-^ M, i = l,...,r, cf. (6). Superficial elements (hence, by reduction,superficial sequences) have been proved as a useful concept in studying Hilbert-Samuel functions and multiplicities, see, for example, ( 18, ch.…”