Algebraic Numbers

Mahima Ranjan Adhikari and Avishek Adhikari
Additional contact information
Mahima Ranjan Adhikari: Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC)
Avishek Adhikari: University of Calcutta, Department of Pure Mathematics

Chapter Chapter 11 in Basic Modern Algebra with Applications, 2014, pp 487-516 from Springer

Abstract: Abstract Chapter 11 introduces algebraic number theory which developed through the attempts of mathematicians to prove Fermat’s Last Theorem. An algebraic number is a complex number which is algebraic over the field Q of rational numbers. An algebraic number field is a subfield of the field C of complex numbers, which is a finite field extension of the field Q and obtained from Q by adjoining a finite number of algebraic elements. The concepts of algebraic numbers, algebraic integers, Gaussian integers, algebraic number fields and quadratic fields are introduced in this chapter after a short discussion on general properties of field extension and finite fields. There are several proofs of Fundamental Theorem of Algebra. It is proved in this chapter by using homotopy (discussed in Chap. 2 ). Moreover, countability of algebraic numbers, existence of transcendental numbers, impossibility of duplication of a general cube and that of trisection of a general angle are shown in this chapter.

Keywords: Finite Field; Fundamental Theorem; Field Extension; Algebraic Number; Algebraic Integer (search for similar items in EconPapers)
Date: 2014
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:978-81-322-1599-8_11

Ordering information: This item can be ordered from
http://www.springer.com/9788132215998

DOI: 10.1007/978-81-322-1599-8_11

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 ().