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Title Details:
Ασκήσεις βασικής άλγεβρας
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.
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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