ACCP Rises to the Polynomial Ring if the Ring has Only Finitely Many Associated Primes

Abstract

We show for a commutative ring R with unity: If R satisfies the ascending chain condition on principal ideals (accp) and has only finitely many associated primes, then for any set of indeterminates X the polynomial ring RX] also satisfies accp. Further we show that accp rises to the power series ring RX]] if R satisfies accp and the ascending chain condition on annihilators.