Adobe PDF (460.07 kB)
Title Details:
Groups - Rings - Polynomials
Authors: Poulakis, Dimitrios
Reviewer: Tzanakis, Nikolaos
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY > COMPUTATIONAL NUMBER THEORY
MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE
MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE > ALGORITHMS AND COMPLEXITY
Keywords:
Computational Number Theory
Group Rings Polynomials
Cyclic Groups
Order Of Element
Irreducible Polynomials
Description:
Abstract:
In Chapter 5 we introduces basic algebraic structures which we shall use in the next chapters. First we consider monoids and we study
theirs basic properties and theirs morphisms. Next, we deal with groups and especially the cyclic groups. We introduce the notion of the order of group elements and of the group morphisms. Finally, we study the rings and fields. Especially, we study the arithmetic in the polynomial ring, the Euclidean division, the irreducible polynomials and the roots of polynomials.
Table of Contents:
Groups - Rings - Polynomials
4.1 Μonoids
4.2 Groups
4.2.1 Definitions - Examples
4.2.2 Subgroups
4.2.3 Order of an Element - Cyclic Groups
4.2.4 Morphisms of Groups
4.3 Rings
4.4 Polynomials
4.4.1 Polynomial Ring
4.4.2 Εuclidean Division of Polynomials
4.4.3 gcd and lcm of Polynomials
4.4.4 Derivative of a Polynomial
4.4.5 Irreducible Polynomials
4.5 Exercices
Bibliography
Technical Editors: Karakostas, Anastasios
Type: Chapter
Creation Date: 2015
Item Details:
License: http://creativecommons.org/licenses/by-nc-nd/3.0/gr
Handle http://hdl.handle.net/11419/1053
Bibliographic Reference: Poulakis, D. (2015). Groups - Rings - Polynomials [Chapter]. In Poulakis, D. 2015. Computational Number Theory [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/1053
Language: Greek
Is Part of: Computational Number Theory
Number of pages 47
Publication Origin: Kallipos, Open Academic Editions