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Torsion-Free Modules Chicago Lectures in Mathematics torsion-free modules Eben Matlis The University of Chicago Press Chicago and London Chicago Lectures in Mathematics Series Irving Kaplansky, Editor The Theory of Sheaves, by Richard G. Swan (1964) Topics in Ring Theory, by I. N. Herstein (1969) Fields and Rings, by Irving Kaplansky (1969; 2d ed. 1972) Infinite Abelian Group Theory, by Phillip A. Griffith (1970) Topics in Operator Theory, by Richard Beals (1971) Lie Algebras and Locally Compact Groups, by Irving Kaplansky (1971) Several Complex Variables, by Raghavan Narasimhan (1971) Torsion-Free Modules, by Eben Matlis (1972) The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 1972 by The University of Chicago All rights reserved Published 1972 Printed in the United States of America ISBN: 0-226-51073-5 (cloth);0-226-51074-3 (paper) Library of Congress Catalog Card Number: 72-95974 TO MAXINE MATLIS CONTENTS Introduction . . . . 1. Cotorsion modules. 9 2. Completions • 17 3. h-local rings . 26 4. Reflexive rings 37 5. Noetherian reflexive rings 47 6. Torsionless rings ..... 57 7. Completely reflexive rings 64 8. Maximal valuation rings .• 73 9. The two generator problem for ideals. 84 10. Noetherian D-rings 97 11. Q.iasi-local D-rings 102 12. h-local D-rings 115 13. Rings of type I. 125 14. Integrally closed D-rings 141 15. Hausdorff D-rings . 156 Bibliography. 164 Index ....• 168 vii

Torsion-free modules PDF

179 Pages·1972·6.603 MB·English

by Eben Matlis

#Mathematics #Algebra

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by Eben Matlis| 1972| 179 pages| 6.603| English

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Author:	Eben Matlis
Publication Year:	1972
ISBN:	9780226510736
Pages:	179
Language:	English
File Size:	6.603
Format:	PDF
Price:	FREE

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