Field Theory

P. M. Cohn
Additional contact information
P. M. Cohn: University College London, Department of Mathematics

Chapter 7 in Basic Algebra, 2003, pp 189-248 from Springer

Abstract: Abstract Fields form one of the basic algebraic concepts, for which there is an extensive theory, dealing mainly with the form taken by field extensions. In Section 7.1 field extensions are described, and the special case of splitting fields is introduced in Section 7.2, leading to the notion of algebraic closure (Section 7.3). In Section 7.4 we examine the problems arising in finite characteristic. One of the main tools in this study is Galois theory and this forms the subject of Sections 7.5 and 7.6, while Sections 7.10 and 7.11 bring its application to the solution of equations . The special case of finite fields is studied in Section 7.8, using information on the roots of unity (Section 7.7); Section 7.9 is devoted to generators and some invariants of extensions.

Keywords: Finite Field; Galois Group; Minimal Polynomial; Galois Theory; Galois Extension (search for similar items in EconPapers)
Date: 2003
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-85729-428-9_7

Ordering information: This item can be ordered from
http://www.springer.com/9780857294289

DOI: 10.1007/978-0-85729-428-9_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().