KERNEL COEFFICIENT IDEALS IN NOETHERIAN-RINGS

A new ideal I, the kernel coefficient ideal of a nonprincipal ideal I , is introduced in a commutative Noetherian ring R. Various properties of this ideal and its relations with many other standard concepts are studied. II is also examined in terms of a sequence of subideals I-n and the relation type of I when R is a local ring. Several characteriz ations of I are given in terms of the kernels of certain ring homomor phisms, and then it is shown that this new ideal has many nice applica tions, especially in the study of asymptotic prime divisors. (C) 1996 Academic Press, Inc.