No abstract

[7] concerning prime divisors of large powers of a fixed element of a commutative Noetherian ring may be generalized and extended to the setting of a Noether lattice. It is shown (Theorem 2.8) that if A is an element of a Noether lattice then all large powers of A have the same prime divisors and (Corollary 3.8) included among this fixed set of primes are those primes that are prime divisors of the integral closure of A k for some k^l. We note that the ring proof of this latter result does not generalize directly since it uses the notion of transcendence degree which to our knowledge has no analogue in multiplicative lattices.Throughout the remainder of this paper, unless otherwise stated, if will denote a Noether lattice [4], and any prime element of if will be assumed to be distinct from /, the greatest element of if. We note that a prime P is a prime divisor of A in X if and only if there is a B in if such that A : B = P. Furthermore, if P is a prime divisor of A then B can be taken to be principal. We will make use of this fact many times throughout this paper.

No abstract

No abstract

No abstract