Abstract
This book has introduced some basic ideas from the part of abstract algebra which deals with fields. Use of these ideas made it relatively easy for us to prove the impossibility of the constructions mentioned in the Introduction.
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Additional Reading for Chapter 9
Computer Algebra: Symbolic Algebraic Computation, ed. B. Buchberger, G.E. Collins, R. Loos and R. Albrecht, Springer-Verlag, Vienna, 2nd edition, 1983.
A. Clark, Elements of Abstract Algebra, Wadsworth, Belmont, California, 1971.
J.H. Davenport, On the Integration of Algebraic Functions, Lecture Notes in Computer Science, 102, Springer-Verlag, Berlin, 1981.
J.B. Fraleigh, A First Course in Abstract Algebra, 3rd edition, Addison-Wesley, Reading, Massachusetts, 1982.
C.R. Hadlock, Field Theory and its Classical Problems, Carus Mathematical Monographs, No. 19, Mathematical Association of America, 1978.
M. Rosenlicht, “Integration in Finite Terms”, American Mathematical Monthly, 79 (1972), 963–972.
T. Rothman, “Genius and Biographers: the Fictionalization of Évariste Galois”, American Mathematical Monthly, 89 (1982), 84–106.
R.H. Risch, “The Solution of the Problem of Integration in Finite Terms”, Transactions of the American Mathematical Society, 76 (1970), 605–608.
L.W. Shapiro, Introduction to Abstract Algebra, McGraw-Hill, New York, 1975.
M. Spivak, Calculus, W.A. Benjamin, New York, 1967.
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© 1991 Springer Science+Business Media New York
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Jones, A., Pearson, K.R., Morris, S.A. (1991). Other Impossibilities and Abstract Algebra. In: Abstract Algebra and Famous Impossibilities. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8552-1_10
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DOI: https://doi.org/10.1007/978-1-4419-8552-1_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97661-7
Online ISBN: 978-1-4419-8552-1
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