Some Topics in Algebra: An Advanced Undergraduate Course at PKU (Mathematical Lectures from Peking University) - Hardcover

Broué, Michel

Hardcover

ISBN 10: 3642412688 ISBN 13: 9783642412684

Publisher: Springer, 2013

Synopsis

During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during and for that course. By no way does it claim to be too exhaustive. It was originally intended as a brief introduction to algebra for an extremely pleasant and passionate audience. It certainly reflects some of the author’s own tastes, and it was influenced by the feelings and the reactions of the students.

Nevertheless, the result covers some advanced undergraduate algebra (rings, ideals, basics of fields theory, algebraic integers, modules, hom and tensor functors, projective modules, etc.) illustrated by numerous examples, counterexamples and exercises. Following a worldwide tradition, the author had planned to conclude by lecturing on the structure of finitely generated modules over principal ideal domains. But during the course, after explaining that the notion of projective modules is more natural than the notion of free modules, it became clear that principal ideal domains needed to be replaced by Dedekind rings; this is much less traditional in the literature ― but not more difficult.

About this title

About the Author

Michel Broué is a distinguished French mathematician specialising in algebra. He is known for his work on modular representations of finite groups (where a famous conjecture bears his name), on the "generic approach" to representations of finite reductive groups, as well as for work on related areas like cyclotomic Hecke algebras. During a career spanning half a century, he has been the editor-in-chief of the Journal of Algebra (2001-2017), the director of the Department of Mathematics and Computer Science of the École Normale Supérieure and the director of the Institut Henri Poincaré (1999-2009).

From the Back Cover

During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during and for that course. By no way does it claim to be to exhaustive. It was originally intended as a brief introduction to algebra for an extremely pleasant and passionate audience. It certainly reflects some of the author’s own tastes, and it was influenced by the feelings and the reactions of the students.

Nevertheless, the result covers some advanced undergraduate algebra (rings, ideals, basics of fields theory, algebraic integers, modules, hom and tensor functors, projective modules, etc…) illustrated by numerous examples, counterexamples and exercises. Following a worldwide tradition, the author had planned to conclude by lecturing on the structure of finitely generated modules over principal ideal domains. But during the course, after explaining that the notion of projective modules is more natural than the notion of free modules, it became clear that principal ideal domains needed to be replaced by Dedekind rings; this is much less traditional in the literature ― but not more difficult.

Edition details

• Publisher: Springer
• Publication date: 2013
• Language: English
• ISBN 10: 3642412688
• ISBN 13: 9783642412684
• Binding: Hardcover
• Number of pages: 201