ACCP rises to the polynomial ring if the ring has only finitely many associated primes. (English) Zbl 1094.13029
Summary: 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 \(R[X]\) also satisfies accp. Further we show that accp rises to the power series ring \(R[[X]]\) if \(R\) satisfies accp and the ascending chain condition on annihilators.
MSC:
| 13E15 | Commutative rings and modules of finite generation or presentation; number of generators |
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
References:
| [1] | DOI: 10.1080/00927879008823937 · Zbl 0729.13017 · doi:10.1080/00927879008823937 |
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