## Commutative rings |

### From inside the book

Try this search over all volumes: **minimal prime ideal**

Results 1-0 of 0

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Prime ideals and the Nullstellensatz | 1 |

The ascending chain condition | 13 |

Zerodivisors | 19 |

7 other sections not shown

### Common terms and phrases

A/xA algebraic Ann(A annihilator assume Auslander-Buchsbaum chains of prime clearly co-dimension coefficients commutative ring complete the proof contains a non-zero contradiction Corollary Dedekind ring defined Definition dimension direct summand discrete valuation ring dR(A elements Exercise exists finite free resolution finite number finitely generated R-module follows free module G-ideal Given grade hence Hilbert ring hypothesis ideal Q induction integral domain integrally closed intersection invertible ideal Krull Lemma little rank Macaulay ring maximal chain maximal ideal maximal R-sequence minimal prime ideal modules with FFR Noetherian ring non-zero prime ideal Note polynomials principal ideal theorem principal prime projective prove PrUfer ring quotient field R-projective R*-free rank Q regular local n-dimensional regular local ring result ring with quotient short exact sequences submodule subring take x e torsion modules unmixedness theorem write x i z(A zero zero-divisors