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Date: 2010-10-25 16:43:03 Algebraic number theory Commutative algebra Field theory Algebraic structures Euclidean domain Euclidean algorithm Algebraic number field Coprime Principal ideal domain Abstract algebra Algebra Ring theory		manuscripta math. Add to Reading List Source URL: www.math.clemson.edu Download Document from Source Website File Size: 211,60 KB Share Document on Facebook

	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 DocID: 1viEZ - View Document
	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 DocID: 1ko90 - View Document
	Sage Reference Manual: General Rings, Ideals, and Morphisms Release 6.7 The Sage Development Team DocID: 1gBWV - View Document
	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 DocID: 1fdZH - View Document
	Sage Reference Manual: Modules Release 6.6.beta0 The Sage Development Team February 21, 2015 DocID: SvyZ - View Document