Methods of Graded Rings

The topic of this book, graded algebra, has developed in the past decade to a vast subject with new applications in noncommutative geometry and physics. Classical aspects relating to group actions and gradings have been complemented by new insights stemming from Hopf algebra theory. Old and new methods are presented in full detail and in a self-contained way. Graduate students as well as researchers in algebra, geometry, will find in this book a useful toolbox. Exercises, with hints for solution, provide a direct link to recent research publications. The book is suitable for courses on Master level or textbook for seminars.

List of contents

The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- InternalHomogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A: Some Category Theory.- Appendix B: Dimensions in an Abelian Category.- Bibliography.- Index.

About the author

Constantin Nastasescu received his Ph. D. at the University of Bucharest in 1970 and became Prof. Titular in 1990. Since 1993 he is a member of the Roumanian Academy of Sciences. He published more than 125 scientific publications in international journals as well as several monographs and books.

Summary

The topic of this book, graded algebra, has developed in the past decade to a vast subject with new applications in noncommutative geometry and physics. Classical aspects relating to group actions and gradings have been complemented by new insights stemming from Hopf algebra theory. Old and new methods are presented in full detail and in a self-contained way. Graduate students as well as researchers in algebra, geometry, will find in this book a useful toolbox. Exercises, with hints for solution, provide a direct link to recent research publications. The book is suitable for courses on Master level or textbook for seminars.

Product details

• Authors: Constanti Nastasescu, Constantin Nastasescu, Fred Van Oystaeyen, Freddy Oystaeyen, Freddy Van Oystaeyen, Freddy Van Oystaeyen
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 26.02.2004
• EAN: 9783540207467
• ISBN: 978-3-540-20746-7
• No. of pages: 306
• Dimensions: 156 mm x 236 mm x 19 mm
• Weight: 484 g
• Illustrations: XIII, 306 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, B, Group Theory, Physics, Mathematics and Statistics, Mathematical physics, Rings (Algebra), Groups & group theory, Group Theory and Generalizations, Mathematical Methods in Physics, Mathematical foundations, Associative rings, Associative Rings and Algebras, Category theory (Mathematics), Category Theory, Homological Algebra, Homological algebra