Title Details: | |
Ασκήσεις βασικής άλγεβρας |
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Authors: |
Beligiannis, Apostolos |
Reviewer: |
Marmaridis, Nikolaos Theodosios |
Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > GENERAL ALGEBRAIC SYSTEMS > ALGEBRAIC STRUCTURES MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > GENERAL ALGEBRAIC SYSTEMS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > COMMUTATIVE ALGEBRA MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > GROUP THEORY AND GENERALIZATIONS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > COMMUTATIVE ALGEBRA > GENERAL COMMUTATIVE RING THEORY MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > GROUP THEORY AND GENERALIZATIONS > FOUNDATIONS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > GROUP THEORY AND GENERALIZATIONS > PERMUTATION GROUPS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > GROUP THEORY AND GENERALIZATIONS > ABSTRACT FINITE GROUPS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > GROUP THEORY AND GENERALIZATIONS > ABELIAN GROUPS |
Keywords: |
Groups
Rings Fields Ideals Homomorphisms Permutations And Symmetry Groups Polynomial Rings Extensions Of Fileds Factorization In Integral Domains Group Actions Rings Of Quotients |
Description: | |
Abstract: |
The book is intended for undergraduate students at Greek universities who are taking a basic algebra course. The book accompanies a standard undergraduate-level basic algebra textbook and aims to help readers through the analytical solution of exercises of varying levels of difficulty, subject matter, and content, to understand the fundamental principles, techniques, and methods of basic algebra. The book is mainly intended for students of mathematics (but also related departments) at Greek universities. The book requires only basic knowledge from other courses, which is summarized, so it can also be used as an aid to understanding the fundamental principles, techniques, and methods of basic algebra by non-specialized readers. It can therefore be used by teachers, students, professionals in the field (professors), and anyone interested in understanding the basic principles of group and ring theory. The main part of the book is devoted to the analytical solution of exercises concerning two of the most fundamental structures of modern algebra, the group structure and the ring structure, as well as their applications. The book is divided into two parts (group theory and ring theory) and 14 chapters. Each chapter of the book develops, without proof, a concise theory that is used to solve the exercises. This is followed by detailed solutions to exercises at various levels (comprehension exercises, computational exercises, theoretical exercises, exercises that extend known results, etc.) related to the concise theory presented. Some of the exercises are accompanied by comments highlighting their relationship to other exercises, to corresponding theoretical topics or extensions thereof, or with references to the literature. Finally, at the end of each chapter, a series of exercises is proposed for solution.
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Linguistic Editors: |
Kioseoglou, Nerina |
Type: |
Undergraduate textbook |
Creation Date: | 11-05-2016 |
Item Details: | |
ISBN |
978-960-603-259-2 |
License: |
http://creativecommons.org/licenses/by-nc-sa/3.0/gr |
DOI | http://dx.doi.org/10.57713/kallipos-712 |
Handle | http://hdl.handle.net/11419/6194 |
Bibliographic Reference: | Beligiannis, A. (2016). Ασκήσεις βασικής άλγεβρας [Undergraduate textbook]. Kallipos, Open Academic Editions. https://dx.doi.org/10.57713/kallipos-712 |
Language: |
Greek |
Consists of: |
1. Ομάδες και υποομάδες 2. Το θεώρημα του Lagrange και οι εφαρμογές του 3. Ομάδες μεταθέσεων 4. Ομάδες-πηλίκα και τα θεωρήματα ισομορφισμών 5. Δακτύλιοι και υποδακτύλιοι 6. Ιδεώδη, δακτύλιοι-πηλίκα και τα θεωρήματα ισομορφισμών 7. Πρώτα και μεγιστοτικά ιδεώδη 8. Δακτύλιοι κυρίων ιδεωδών και περιοχές μονοσήμαντης ανάλυσης 9. Δακτύλιοι πολυωνύμων και σώματα κλασμάτων 10. Σχέσεις ισοδυναμίας, πράξεις και μονοειδή |
Number of pages |
450 |
Publication Origin: |
Kallipos, Open Academic Editions |
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