… is an associated prime of a principal ideal of D}, we prove a theorem on the finiteness of the
ideal transform. It is also shown that the … Ds is an associated prime of a principal ideal of Ds} …

… Namely, we shall show that the principal component a(p) of a belonging … ideal g is a minimal
prime ideal in a ring with maximal condition, then g is primary, for its associated prime ideals …

… associated prime ideal of a principal ideal in R[X] has height one if and only if each associated
prime ideal of a principal ideal … Krull’s principal ideal theorem [7, Theorem 142] states that …

… associated primes which appear in the literature, we show, in Section 2, that unlike the Nagata
primes and weak Bourbaki primes, the Krull primes … is minimal over a principal ideal of R. …

… and lower principal component ideals of A, … ) associated prime ideals of A. Thus we see
that for a ring with unit element and ACC for ideals, the two definitions of associated prime ideals …

… For this purpose we define the set Ass(A) of associated primes of the ideal A to be those …
3] of whether for a maximal prime divisor P of an ideal A the principal P-component A(P) is …

… a general Prime Ideal Principle for proving that certain ideals in a commutative ring are prime.
This … Following (3.16), we will write F1 for the family of principal ideals in a (given) ring R. …

… different definitions of the associated primes of an ideal (eg, … an associated prime of an ideal
I in a ring R if P is a minimal … primes and each of them is isolated, every principal ideal of a …

… prime associated with A, then A(P) is called a principal … ordered set of (right) associated prime
ideals of A. Thus we see that … for ideals, the two definitions of associated prime ideals of an …

… concerned with the associated primes of principal ideals of R … first key result about associated
primes of principal ideals. … a prime ideal of R and assume that P is an associated prime of …