Polynomials over Z_n
Basics and results on solvable polynomials
(Sprache: Englisch)
Polynomials are a classical subject of mathematics. The first step towards theabstract concept of polynomials was the investigation of real and complexfunctions.During the last century studies on polynomials over commutativerings with identity gave rise for...
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Polynomials are a classical subject of mathematics. The first step towards the
abstract concept of polynomials was the investigation of real and complex
functions.During the last century studies on polynomials over commutative
rings with identity gave rise for researches on polynomials over other classes
of algebraic structures, such as groups, semigroups,lattices, rings (with or
without identity), etc.. The purpose of this work is to give an overview of
polynomials over commutative rings with identity and especially over the ring
Z_n, the residue classes modulo n. Besides basic definitions and well-known
results,the reader will be introduced to aspects of the abstract theory of
polynomials to have results for the solvability of a polynomial equation of the
form f = 0 over a variety V. This will be the basis to establish results when a
polynomial equation f = 0 over the ring Z_n has got a solution in Z_n or in an
extension ring of Z_n. Further more, the reader will find results on reducible
and irreducible polynomials over Z_n. The last chapters deal with the Galois
theory for finite local commutative rings and we will see when the factor ring
Z_n[x]/(f) is the smallest extension ring of Z_n. Eventually, the reader will get
to know some results when a function f from Z_n to Z_n can be represented
as a polynomial function over Z_n. The book addresses to students who are
interested in the subject as well as all interested people who want to get
familiar with the most important aspects of the theory of polynomials and
especially with polynomials over Z_n.
Autoren-Porträt von Jörg Forstner
Jörg Forstner, Dipl.Ing.:Studied Technical Mathematics at the JohannesKepler Universität Linz, Austria,from October 1999until May 2005. Talk at the conference AAA (69.Arbeitstagung Allgemeine Algebra) in March 2005.Application Engineer for SIEMENS VAI in Linz,Austria, for 1.5 years.
Bibliographische Angaben
- Autor: Jörg Forstner
- 2007, Maße: 17 x 24 cm, Kartoniert (TB), Englisch
- Verlag: VDM Verlag Dr. Müller
- ISBN-10: 3836424339
- ISBN-13: 9783836424332
Sprache:
Englisch
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