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Noetherian ring
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31	Algebraic Geometry I Fall 2013 Eduard Looijenga Rings are always supposed to possess a unit element 1 and a ring homomorphism will always take unit to unit. We allow that 1 = 0, but in that case we get of course the zer Add to Reading List Source URL: www.staff.science.uu.nl Language: English - Date: 2013-12-26 23:18:31 Irreducible component Ideal Unique factorization domain Prime ideal Ring Algebraic variety Noetherian topological space Zariski topology Polynomial ring Abstract algebra Algebra Ring theory
32	Chapter 5 Dimension Theory The geometric notion of the dimension of an aﬃne algebraic variety V is closely related to algebraic properties of the coordinate ring of the variety, that is, the ring of polynomial functio Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2007-06-09 11:06:04 Ring theory Module theory Algebraic structures Ideals Noetherian ring Commutative ring Hilbert series and Hilbert polynomial Dedekind domain Krull dimension Abstract algebra Algebra Commutative algebra
33	Exercises Chapter 1 1. What are the primary ideals of Z? 2. Let R = k[x, y] where k is a ﬁeld. Show that Q = (x, y 2 ) is P -primary, and identify P. 3. Continuing Problem 2, show that Q is not a power of a prime ideal Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2007-06-09 00:09:54 Commutative algebra Algebraic structures Module theory Localization Local ring Completion Noetherian ring Ideal Ring Abstract algebra Algebra Ring theory
34	Chapter 1 Primary Decomposition and Associated Primes[removed] Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2009-10-14 11:55:44 Commutative algebra Ring theory Ideals Algebraic structures Associated prime Lasker–Noether theorem Noetherian ring Annihilator Primary ideal Abstract algebra Algebra Module theory
35	Chapter 6 Depth 6.1 Systems of Parameters Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2007-06-06 11:22:53 Commutative algebra Module theory Homological algebra Dimension Depth Noetherian ring Regular local ring Krull dimension Ring Abstract algebra Algebra Ring theory
36	D. Eisenbud and E. G. Evans, Jr. Nagoya Math. J. Vol[removed]), 41-53 A GENERALIZED PRINCIPAL IDEAL THEOREM DAVID EISENBUD* AND E. GRAHAM EVANS, JR.* Add to Reading List Source URL: www.msri.org Language: English - Date: 2005-11-04 13:11:39 Ring theory Module theory Prime ideals Ideals Finitely-generated module Depth Polynomial ring Noetherian ring Commutative ring Abstract algebra Algebra Commutative algebra
37	JOURNAL 16, [removed]OF ALGEBRA Add to Reading List Source URL: www.msri.org Language: English - Date: 2005-09-02 18:47:57 Commutative algebra Ideals Algebraic structures Module theory Serial module Principal ideal ring Idempotence Noetherian ring Finitely-generated module Abstract algebra Algebra Ring theory
38	David Eisenbud Nagoya Math. J. Vol[removed]), 61-67 ADIC APPROXIMATION OF COMPLEXES, AND MULTIPLICITIES Add to Reading List Source URL: www.msri.org Language: English - Date: 2005-09-09 17:21:33 Ring theory Module theory Homological algebra Group theory Spectral sequence Completion Noetherian ring Ring Finitely-generated module Abstract algebra Algebra Commutative algebra
39	PDF Document Add to Reading List Source URL: www.msri.org Language: English - Date: 2005-09-16 13:13:09 Ring theory Algebraic structures Cohen–Macaulay ring Depth Polynomial ring Commutative ring Ring Ideal Noetherian ring Abstract algebra Algebra Commutative algebra
40	JOURNAL OF ALGEBRA 27, [removed]Generating Theorems Add to Reading List Source URL: www.msri.org Language: English - Date: 2005-09-09 17:20:49 Module theory Ring theory Homological algebra Algebraic structures Finitely-generated module Projective module Local ring Torsion Noetherian ring Abstract algebra Algebra Commutative algebra

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