- Summary
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This book is the French translation of the classic A Course in Constructive Algebra (1988). It presents the basic notions of modern algebra from a constructive point of view.
Mathematical objects are not limited to a restricted class of “constructive objects”.
Constructive algebra is a generalisation of classical algebra in that we do not assume the law of the excluded middle. Every theorem in this book can therefore be understood as referring to the conventional universe of mathematical discourse, and the proofs are correct in this universe. The pleasant surprise is that the constructive proof, normally more precise, is in many cases simpler. - Contents
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Préface
Ensembles
Algèbre de base
Anneaux et modules
Divisibilité dans les anneaux intègres
Anneaux principaux
Théorie des corps
Factorisation des polynômes
Anneaux commutatifs noethériens
Algèbres de dimension finie
Groupes libres
Groupes abéliens
Théorie des valeurs absolues
Domaines de Dedekind
Références
Index
Postface
- Author (s)
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Ray MINESRay Mines, Department of Mathematical Sciences, New Mexico State University, Las Cruces, USAFred RICHMANFred Richman, Department of Mathematical Sciences, New Mexico State University, Las Cruces, USAWim RUITENBURG AuteurWim Ruitenburg, Department of Mathematics, Statistics, and Computer Science, Marquette University,Milwaukee, USAHenri LOMBARDI (transl. by)Henri Lombardi, accreditation to supervise research, hosted in Dept of Mathematics, University of Franche-Comté, Besançon, FranceStefan NEUWIRTH (with the coll. of)Stefan Stefan NEUWIRTH, lecturer, Mathematics Laboratory of Besançon (UMR 6623), University of Franche-Comté, France
- Readership
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University profesors, students and high school teachers
- downloadable items
- Reviews and press reviews
- Online
- Support (s)
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Laboratoire de mathématiques de Besançon (UMR 6623)
