About this book
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative.
The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century.
This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors, and theoretical computer scientists.
- DOI https://doi.org/10.1007/978-94-017-9944-7
- Copyright Information Springer Science+Business Media Dordrecht 2015
- Publisher Name Springer, Dordrecht
- eBook Packages Mathematics and Statistics
- Print ISBN 978-94-017-9943-0
- Online ISBN 978-94-017-9944-7
- Series Print ISSN 1572-5553
- Series Online ISSN 2192-2950
- About this book