ENGLISH

Skew fields: theory of general division rings

By P. M. Cohn FRS

Book information

Publisher
Cambridge University Press
Year
1995
ISBN
0521432170, 9780521432177
LCC
QA251.5 .C633 1995
Open Library ID
OL787891M
Language
english
Format
DJVU
Filesize
5 MB (4945037 bytes)
Series
Encyclopedia of mathematics and its applications 57
Pages
258\258
Library
kolxoz
DPI
300
Scanned
landscape
Time added
2009-07-20 03:45:11

Description

Algebraists have studied noncommutative fields (also called skew fields or division rings) less thoroughly than their commutative counterparts. Most existing accounts have been confined to division algebras, i.e. skew fields that are finite dimensional over their center. This work offers the first comprehensive account of skew fields. It is based on the author's LMS Lecture Note Volume "Skew Field Constructions". The axiomatic foundation and a precise description of the embedding problem precedes an account of algebraic and topological construction methods. The author presents his general embedding theory with full proofs, leading to the construction of skew fields. The author has simplified his treatment of equations over skew fields and has extended it by the use of matrix methods. A separate chapter describes valuations and orderings on skew fields, with a construction applicable to free fields. Numerous exercises test the reader's understanding, presenting further aspects and open problems in concise form. Notes and comments at the end of chapters provide historical background. The book will appeal to researchers in algebra, logic, and algebraic geometry, as well as graduate students in these fields.

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