| Algebraic Patching 2011 Edition Contributor(s): Jarden, Moshe (Author) |
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ISBN: 3642266517 ISBN-13: 9783642266515 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: February 2013 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - General - Mathematics | Group Theory - Mathematics | Algebra - Abstract |
| Dewey: 512 |
| Series: Springer Monographs in Mathematics |
| Physical Information: 0.66" H x 6.14" W x 9.21" (0.98 lbs) 292 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 $C$. |