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| Title Details: | |
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Groups - Rings - Polynomials |
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| 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 |