ON THE EMBEDDED PRIMARY COMPONENTS OF IDEALS .1.

It is well known that an embedded primary component of an ideal I in a Noetherian ring R is not uniquely determined by 1. Our main results a re concerned with these embedded primary components of I. Specifically , they concern the maximal M-primary components of a non-open ideal I in a local ring (R, M). We show that if J is any ideal between I and a maximal M-primary component of I, then J is the intersection of the m aximal M-primary components of I that contain J. Also, we characterize the sum of all the maximal M-primary components of I, show that one m aximal M-primary component of I is irreducible if and only if all are, and then show that some other standard properties of M-primary ideals (length, number of generators, etc.) are not shared by different maxi mal M-primary components of I. (C) 1994 Academic Press, Inc.