Abstract :
A new idealI*, the kernel coefficient ideal of a nonprincipal idealI, is introduced in a commutative Noetherian ringR. Various properties of this ideal and its relations with many other standard concepts are studied.I* is also examined in terms of a sequence of subidealsInand the relation type ofIwhenRis a local ring. Several characterizations ofI* are given in terms of the kernels of certain ring homomorphisms, and then it is shown that this new ideal has many nice applications, especially in the study of asymptotic prime divisors.
