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Principal ideal domain
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1	CATEGORIES AND HOMOLOGICAL ALGEBRA Exercises for April 26 Exercise 1. Let R be a principal ideal domain. If M is a finitely generated R-module, show that M is a projective R-module ⇐⇒ M is a free R-module ⇐⇒ M is Add to Reading List Source URL: www.math.ru.nl Language: English - Date: 2018-05-17 10:22:49
2	Finitely Generated p-Primary Modules over PIDs E. L. Lady ASSUMPTIONS. R is a principal ideal domain and (p) is a prime ideal. M is a module such that pk M = 0 and pk−1 M 6= 0 . Furthermore m ∈ M is such that pk−1 Add to Reading List Source URL: www.math.hawaii.edu Language: English - Date: 2001-04-07 05:36:01
3	Sage Reference Manual: General Rings, Ideals, and Morphisms Release 6.7 The Sage Development Team Add to Reading List Source URL: doc.sagemath.org Language: English - Date: 2015-06-24 05:21:38 Ring theory Algebraic structures Dedekind domain Ring Commutative ring Krull dimension Principal ideal domain Principal ideal Polynomial ring Abstract algebra Algebra Commutative algebra
4	MATH 210A PRACTICE MIDTERM 1. √ Recall that the Gaussian integers Z[i] form a euclidean domain (with norm \|a + bi\| = a2 + b2 ), and thus a principal ideal domain. State the classification theorem for finitelygenerated Add to Reading List Source URL: math.stanford.edu - Date: 2014-11-02 19:33:32
5	Sage Reference Manual: Modules Release 6.6.beta0 The Sage Development Team February 21, 2015 Add to Reading List Source URL: sagemath.org Language: English - Date: 2015-02-21 07:35:21 Module theory Linear algebra Vectors Algebraic structures Finitely-generated module Module Vector space D-module Structure theorem for finitely generated modules over a principal ideal domain Algebra Abstract algebra Mathematics
6	FACTORIZATION IN INTEGRAL DOMAINS PETE L. CLARK Contents Classical Roots – The Fundamental theorem of Arithmetic Basic Terminology Add to Reading List Source URL: math.uga.edu Language: English - Date: 2012-08-04 19:41:41 Commutative algebra Unique factorization domain Integral domain Atomic domain Euclidean domain Ideal class group Ascending chain condition on principal ideals Ring Principal ideal domain Abstract algebra Algebra Ring theory
7	Chapter 6 Dedekind Schemes In this chapter we introduce the main protagonists of the following two chapters, namely Dedekind schemes. These will be schemes characterised by certain special properties that are common to Add to Reading List Source URL: www.renyi.hu Language: English - Date: 2007-09-28 04:05:10 Ring theory Dedekind domain Integrally closed domain Integral element Discrete valuation ring Principal ideal domain Valuation ring Finitely-generated module Local ring Abstract algebra Algebra Commutative algebra
8	THE EUCLIDEAN ALGORITHM IN ALGEBRAIC NUMBER FIELDS FRANZ LEMMERMEYER Abstract. This article, which is an update of a version published 1995 in Expo. Math., intends to survey what is known about Euclidean number fields; Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2004-02-13 18:30:23 Ring theory Commutative algebra Euclidean algorithm Linear algebra Greatest common divisor Norm Principal ideal domain Euclidean domain Abstract algebra Algebra Mathematics
9	JOURNAL OFALGEBRA 16,[removed]Modules Over Dedekind DAVID Add to Reading List Source URL: www.msri.org Language: English - Date: 2005-09-02 18:46:24 Ring theory Commutative algebra Algebraic structures Homological algebra Dedekind domain Finitely-generated module Projective module Ideal Principal ideal ring Abstract algebra Algebra Module theory
10	Sage Reference Manual: Modules Release 6.3 The Sage Development Team August 11, 2014 Add to Reading List Source URL: www.sagemath.org Language: English - Date: 2014-11-16 14:58:22 Module theory Finitely-generated module Module D-module Vector space Structure theorem for finitely generated modules over a principal ideal domain Algebraic structure Endomorphism ring Sage Algebra Abstract algebra Mathematics

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