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Algebraic Patching (Springer Monographs in Mathematics)

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Algebraic Patching (Springer Monographs in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$.

Synopsis:

This book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields".

About the Author

Moshe Jarden was born in 1942 in Tel Aviv, Israel. In 1970 he received his Ph.D in Mathematics from the Hebrew University of Jerusalem having Hillel Furstenberg as his thesis advisor. He spent three years (1972-1974) at the Mathematisches Institut of Heidelberg with Peter Roquette as his mentor and habilitated there in 1972. The years he spent in Heidelberg laid the foundation to a long termed cooperation with German mathematicians, especially with Peter Roquette, Wulf-Dieter Geyer, Gerhard Frey, and Juergen Ritter. As a token to his achievements in Mathematics and his fruitful cooperation with German mathematicians the Alexander von Humboldt Foundation granted Jarden in 2001 the L. Meithner-A.v.Humboldt Prize. In the autumn of 1974 Jarden returned to Israel and joined the School of Mathematics of Tel Aviv University, where he became a full professor in 1982 and the incumbent of the Cissie and Aaron Beare chair in Algebra and Number Theory in 1998. Jointly with Michael Fried, Jarden published the book "Field Arithmetic" in the series Ergebnisse der Mathematik und ihrer Grenzgebiete of Springer. He won the Landau Prize for the publication of that book. Moshe Jarden inherited his love to Mathematics from his father Dr. Dov Jarden who was both a Hebrew linguistic and a mathematician. He is married to Rina, has three daughters Kmeha, Hemyat, and Uri, and a son Guy. He also has thirteen grandchildren and lives in Mevasseret Zion, near Jerusalem.

Table of Contents

1. Algebraic Patching.- 2. Normed Rings.- 3. Several Variables.- 4. Constant Split Embedding Problems over Complete Fields.- 5. Ample Fields.- 6. Non-Ample Fields.- 7. Split Embedding Problems over Complete Fields.- 8. Split Embedding Problems over Ample Fields.- 9. The Absolute Galois Group of C(t).- 10. Semi-Free Profinite Groups.- 11. Function Fields of One Variable over PAC Fields.- 12. Complete Noetherian Domains.- Open Problems.- References.- Glossary of Notation.- Index.

Product Details

ISBN:
9783642266515
Author:
Jarden, Moshe
Publisher:
Springer
Location:
Berlin, Heidelberg
Subject:
Algebra - General
Subject:
Absolute Galois Group
Subject:
Ample Field
Subject:
Field Arithmetic
Subject:
Finite Split Embedding Problem
Subject:
Free Profinite Group
Subject:
Algebra
Subject:
Field Theory and Polynomials
Subject:
Group Theory and Generalizations
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Field theory (physics)
Subject:
Group Theory
Subject:
Mathematics - Algebra
Copyright:
Edition Description:
2011
Series:
Springer Monographs in Mathematics
Publication Date:
20130224
Binding:
TRADE PAPER
Language:
English
Pages:
300
Dimensions:
235 x 155 mm 486 gr

Related Subjects

Science and Mathematics » Chemistry » Physical Chemistry
Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Group Theory

Algebraic Patching (Springer Monographs in Mathematics) New Trade Paper
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Product details 300 pages Springer - English 9783642266515 Reviews:
"Synopsis" by , This book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields".
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