Advanced Algebra. Selected References, Digital Second Edition. Anthony W. Knapp. DOI: /euclid/

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1 Selected References, DOI: /euclid/ from Advanced Algebra Digital Second Edition Anthony W. Knapp Full Book DOI: /euclid/ ISBN: Distributed by Project Euclid. For copyright information, see the following page.

2 Anthony W. Knapp 81 Upper Sheep Pasture Road East Setauket, N.Y , U.S.A. to: Homepage: aknapp Title: Advanced Algebra Cover: Content of the Snake Lemma; see page 185. Mathematics Subject Classification (2010): 11 01, 13 01, 14 01, 16 01, 18G99, 55U99, 11R04, 11S15, 12F99, 14A05, 14H05, 12Y05, 14A10, 14Q99. First Edition, ISBN c 2007 Anthony W. Knapp Published by Birkhäuser Boston Digital Second Edition, not to be sold, no ISBN c 2016 Anthony W. Knapp Published by the Author All rights reserved. This file is a digital second edition of the above named book. The text, images, and other data contained in this file, which is in portable document format (PDF), are proprietary to the author, and the author retains all rights, including copyright, in them. The use in this file of trade names, trademarks, service marks, and similar items, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. All rights to print media for the first edition of this book have been licensed to Birkhäuser Boston, c/o Springer Science+Business Media Inc., 233 Spring Street, New York, NY 10013, USA, and this organization and its successor licensees may have certain rights concerning print media for the digital second edition. The author has retained all rights worldwide concerning digital media for both the first edition and the digital second edition. The file is made available for limited noncommercial use for purposes of education, scholarship, and research, and for these purposes only, or for fair use as understood in the United States copyright law. Users may freely download this file for their own use and may store it, post it online, and transmit it digitally for purposes of education, scholarship, and research. They may not convert it from PDF to any other format (e.g., EPUB), they may not edit it, and they may not do reverse engineering with it. In transmitting the file to others or posting it online, users must charge no fee, nor may they include the file in any collection of files for which a fee is charged. Any exception to these rules requires written permission from the author. Except as provided by fair use provisions of the United States copyright law, no extracts or quotations from this file may be used that do not consist of whole pages unless permission has been granted by the author (and by Birkhäuser Boston if appropriate). The permission granted for use of the whole file and the prohibition against charging fees extend to any partial file that contains only whole pages from this file, except that the copyright notice on this page must be included in any partial file that does not consist exclusively of the front cover page. Such a partial file shall not be included in any derivative work unless permission has been granted by the author (and by Birkhäuser Boston if appropriate). Inquiries concerning print copies of either edition should be directed to Springer Science+Business Media Inc.

3 SELECTED REFERENCES Artin, E., Theory of Algebraic Numbers, notes by Gerhard Würges, George Striker, Göttingen, Artin, E., C. J. Nesbitt, and R. M. Thrall, Rings with Minimum Condition, University of Michigan Press, Ann Arbor, Atiyah, M. F., and I. G. Macdonald, Introduction to Commutative Algebra, Addison- Wesley Publishing Company, Reading, MA, Borevich, Z. I., and I. R. Shafarevich, Number Theory, Academic Press, New York, Brieskorn, E., and H. Knörrer, Plane Algebraic Curves, Birkhäuser, Basel, Brown, K. S., Cohmology of Groups, Springer-Verlag, New York, Buchberger, B. and F. Winkler (eds.), Gröbner Bases and Applications, Cambridge University Press, Cambridge, Buell, D. A., Binary Quadratic Forms, Springer-Verlag, New York, Cartan, H., and S. Eilenberg, Homological Algebra, Princeton University Press, Princeton, Cassels, J. W. S., Rational Quadratic Forms, Academic Press, London, Cassels, J. W. S., and A. Fröhlich (eds.), Algebraic Number Theory, Academic Press, London, Cohn, H., A Classical Invitation to Algebraic Numbers and Class Fields, Springer- Verlag, New York, Cox, D. A., Primes of the Form x 2 + ny 2, John Wiley & Sons, New York, Cox, D., J. Little, and D. O Shea, Ideals, Varieties, and Algorithms, Springer-Verlag, New York, Dirichlet, P. G. L., Lectures on Number Theory, supplements by R. Dedekind, English translation of the original German, American Mathematical Society, Providence, Dummit, D. S., and R. M. Foote, Abstract Algebra, Prentice Hall, Englewood Cliffs, NJ, 1991; second edition, Upper Saddle River, NJ, 1999; third edition, John Wiley & Sons, Hoboken, NJ, Eisenbud, D., Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, New York, Eisenbud, D., and J. Harris, The Geometry of Schemes, Springer-Verlag, New York, Farb, B., and R. K. Dennis, Noncommutative Algebra, Springer-Verlag, New York,

4 714 Selected References Farkas, H. M., and I. Kra, Riemann Surfaces, Springer-Verlag, New York, 1980; second edition, Freyd, P., Abelian Categories: An Introduction to the Theory of Functors, Harper and Row, New York, Fröhlich, A., and M. J. Taylor, Algebraic Number Theory, Cambridge University Press, Cambridge, Fulton, W., Algebraic Curves: An Introduction to Algebraic Geometry, Addison- Wesley Publishing Company, Redwood City, CA, 1989; originally published by W. A. Benjamin, Inc., New York, 1969, and reprinted in Gauss, C. F., Disquisitiones Arithmeticae, English translation of the original Latin, Springer-Verlag, New York, Griffiths, P. A., Introduction to Algebraic Curves, American Mathematical Society, Providence, Gunning, R. C., Introduction to Holomorphic Functions of Several Variables, Volume III: Homological Theory, Wadsworth &Brooks/Cole, Pacific Grove, CA, Hall, M., The Theory of Groups, The Macmillan Company, New York, Hardy, G. H., and E. M. Wright, An Introduction to the Theory of Numbers, Clarendon Press, Oxford, 1938; second edition, 1945; third edition, 1954; fourth edition, 1960; fifth edition, Harris, J., Algebraic Geometry: A First Course, Springer-Verlag, New York, 1992; reprinted with corrections, Hartshorne, R., Algebraic Geometry, Springer-Verlag, New York, Hasse, H., Number Theory, English translation of the original German, Springer- Verlag, Berlin, 1980; reprinted, Hecke, E., Lectures on the Theory of Algebraic Numbers, English translation of the original German, Springer-Verlag, New York, Hilton, P. J., and U. Stammbach, A Course in Homological Algebra, Springer-Verlag, New York, 1971; second edition, Hua, L.-K., Introduction to Number Theory, English translation of the original Chinese, Springer-Verlag, Berlin, Hungerford, T. W., Algebra, Holt, Rinehart and Winston, New York, 1974; reprinted, Springer-Verlag, New York, 1980; reprinted with corrections, Ireland, K., and M. Rosen A Classical Introduction to Modern Number Theory, Springer-Verlag, New York, 1982; second edition, Jacobson, N., Basic Algebra, Volume I, W. H. Freeman and Co., San Francisco, 1974; second edition, New York, Volume II, W. H. Freeman and Co., San Francisco, 1980; second edition, New York, Jacobson, N., Lectures in Abstract Algebra, Volume I, D. Van Nostrand Company, Inc., Princeton, 1951; reprinted, Springer-Verlag, New York, Volume II, D. Van Nostrand Company, Inc., Princeton, 1953; reprinted, Springer-Verlag, New York, Volume III, D. Van Nostrand Company, Inc., Princeton, 1964; reprinted, Springer-Verlag, New York, 1975.

5 Selected References 715 Jacobson, N., Structure of Rings, American Mathematical Society, Providence, 1956; revised edition, Jacobson, N., The Theory of Rings, American Mathematical Society, New York, 1943; multiple reprintings, American Mathematical Society, Providence. Knapp, A. W., Elliptic Curves, Princeton University Press, Princeton, Knapp, A. W., Basic Real Analysis, Birkhäuser, Boston, Knapp, A. W., Advanced Real Analysis, Birkhäuser, Boston, Knapp, A. W., Basic Algebra, Birkhäuser, Boston, 2006; digital second edition, Knapp, A. W., and D. A. Vogan, Cohomological Induction and Unitary Representations, Princeton University Press, Princeton, Lam, T. Y., A First Course in Noncommutative Rings, Springer-Verlag, New York, 1991; second edition, Lang, S., Algebra, Addison-Wesley, Reading, MA, 1965; second edition, 1984; third edition, 1993; revised third edition, Springer, New York, Lang, S., Algebraic Number Theory, Addison-Wesley, Reading, MA, 1970; reprinted, Springer-Verlag, New York, 1986; second edition, Lang, S., Introduction to Algebraic and Abelian Functions, Addison-Wesley, Reading, MA, 1972; second edition, Springer-Verlag, New York, 1982; reprinted, Mac Lane, S., Categories for the Working Mathematician, Springer, New York, 1971; second edition, Macdonald, I. G., Algebraic Geometry: Introduction to Schemes, W. A. Benjamin, Inc., New York, Massey, W. S., Singular Homology Theory, Springer-Verlag, New York, Matsumura, H., Commutative Algebra, W. A. Benjamin, Inc., New York, 1970; second edition, Benjamin-Cummings, Reading, MA, Matsumura, H., Commutative Ring Theory, Cambridge University Press, Cambridge, 1986; reprinted with corrections, Muir, T., The Theory of Determinants in the Historical Order of Development, Volume I, Macmillan, London, 1906; Volume II, 1911; Volume III, 1920; Volume IV, 1923; Volume V, Reprint of Volumes I II, Dover Publications, New York, 1960; reprint of Volumes III IV, Mumford, D., The Red Book of Varieties and Schemes, Lecture Notes in Mathematics, Volume 1358, Springer-Verlag, Berlin, 1988; second expanded edition, Niven, I., and H. S. Zuckerman, An Introduction to the Theory of Numbers, John Wiley & Sons, New York, 1960; second edition, 1966; third edition, 1972; fourth edition, 1980; fifth edition, with H. L. Montgomery, Reid, M., Undergraduate Algebraic Geometry, Cambridge University Press, Cambridge, Rotman, J. J., Notes on Homological Algebras, Van Nostrand Reinhold Company, New York, Rudin, W., Principles of Mathematical Analysis, McGraw Hill Book Company, New York, 1953; second edition, 1964; third edition 1976.

6 716 Selected References St. Andrews, School of Mathematics and Statistics, University of St. Andrews, Scotland, MacTutor History of Mathematics Archive, Biographies of Mathematicians, for background, for entry point, BiogIndex.html for indices of biographies of mathematicians, updated as of Serre, J.-P., Algèbre Locale, Multiplicités, second edition, Lecture Notes in Mathematics, Volume 11, Springer-Verlag, Berlin, Serre, J.-P., A Course in Arithmetic, Springer-Verlag, New York, Serre, J.-P., Local Fields, Springer-Verlag, New York, Shafarevich, I. R., Basic Algebraic Geometry, Springer-Verlag, Berlin, 1977; second edition, published as two volumes, Silverman, J. H., The Arithmetic of Elliptic Curves, Springer-Verlag, New York, Sturmfels, B., What is a Gröbner basis?, Notices of the American Mathematical Society 52 (2005), University of Sydney, Representation and monomial orders, Handbook of Magma Computer Algebra System, magma/handbook/text/1177, updated as of Ueno, K., An Introduction to Algebraic Geometry, American Mathematical Society, Providence, Van der Waerden, B. L., Modern Algebra, English translation of the original German, Volume I, Frederick Ungar Publishing Co., New York, Volume II, Frederick Ungar Publishing Co., New York, Villa Salvador, G. D., Topics in the Theory of Algebraic Function Fields, Birkhäuser, Boston, Walker, R. J., Algebraic Curves, Princeton University Press, Princeton, 1950; reprinted, Dover Publications, New York, 1962; reprinted, Springer-Verlag, New York, Weil, A., Basic Number Theory, Springer-Verlag, New York, 1967; second edition, 1973; third edition, 1974; reprinted, Weil, A., Number Theory: An Approach through History: From Hammurapi to Legendre, Birkhäuser, Boston, 1984; reprinted, Zariski, O., and P. Samuel, Commutative Algebra, Volume I, D. Van Nostrand Co., Inc., Princeton, 1958; reprinted, Springer-Verlag, New York, Volume II, D. Van Nostrand Co., Inc., Princeton, 1960; reprinted, Springer-Verlag, New York, 1976.