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

Über die Autorin bzw. den Autor

Michel Broué is Emeritus Exceptional Professor of Mathematics at the University Paris-Diderot Paris 7. He has been the Director of the Institut Henri-Poincaré in Paris (1999-2009), and the Director of the Department of Mathematics and Computer Science (DMI) at the École normale supérieure (1986-1993) He is a Foreign Honorary Member of the American Academy of Arts and Sciences, a Fellow of the American Mathematical Society, a Senior Member of the Institut Universitaire de France, and a frequent visitor to many institutions in the world. He is the Editor-in-chief of the Journal of Algebra, and a member of several editorial boards. His main research area is Algebra and Representation Theory, in particular of finite and algebraic groups.

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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.