Foundations of algebra and number theory
type: Item
instance of: scholarly article
title: Foundations of algebra and number theory
zbMATH Open document ID: 1388.00004
DOI: 10.1007/978-3-662-45229-5
author: Janko Böhm
published in: Springer-Lehrbuch
publication date: 2017-08-17T00:00:00Z
review text: This textbook on foundations of algebra and number theory contains almost 350 pages. The chapters of the book are entitled: (1) Introduction; (2) Integers; (3) Groups; (4) Rings; (5) Modules and elementary divisors; (6) Groups of reduced residues; (7) Fields; (8) Quadratic residues; (9) Constructions with ruler and compass. The material covered in the algebraic part is very extensive and also comprehends more advanced topics like Galois theory, Noetherian rings and finitely generated modules over principal ideal domains. A very positive aspect of the book is the illustration of the concepts by many examples. Especially remarkable is the extensive discussion of symmetry groups of graphs and of geometrical objects. Also the algorithmic aspects and applications to cryptography get broad coverage. There are a few things the reviewer would have liked to have seen altered. For example basic applications of the theory of modules to algebraic number theory could have been added without substantially increasing the volume of the book. All in all this book is a valuable addition to the literature.
reviewed by: Helmut Maier
Mathematics Subject Classification ID: 00A05
Mathematics Subject Classification ID: 11-01
Mathematics Subject Classification ID: 12-01
Mathematics Subject Classification ID: 20-01
Mathematics Subject Classification ID: 13-01
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 6761900
zbMATH Keywords: algebra
zbMATH Keywords: number theory
zbMATH Keywords: cryptography
describes a project that uses: SINGULAR
describes a project that uses: Surfer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-662-45229-5
OpenAlex ID: W2492611452
description: scientific article; zbMATH DE number 6761900