Andy R. Magid - Böcker

Knowledge of an analytic group implies knowledge of its module category. However complete knowledge of the category does not determine the group. Professor Magid shows here that the category determines another, larger group and an algebra of functions in this new group. The new group and its function algebra are completely described; this description thus tells everything that is known when the module category, as a category, is given. This categorical view brings together and highlights the significance of earlier work in this area by several authors, as well as yielding new results. By including many examples and computations Professor Magid has written a complete account of the subject that is accessible to a wide audience. Graduate students and professionals who have some knowledge of algebraic groups, Lie groups and Lie algebras will find this a useful and interesting text.

"Presenting the proceedings of a conference held recently at Northwestern University, Evanston, Illinois, on the occasion of the retirement of noted mathematician Daniel Zelinsky, this novel reference provides up-to-date coverage of topics in commutative and noncommutative ring extensions, especially those involving issues of separability, Galois theory, and cohomology."

Differential Modules over Differential Rings provides an introduction and reference for researchers in commutative and differential algebra and could be used as the basis for a graduate course or seminar. The book is best suited to an audience for whom the terminology of rings, modules, homomorphisms, and categories is already familiar. Although the topic is rooted in differential algebra, and the book should be of interest to workers in that area, no particular prior knowledge of differential algebra is assumed. When it is necessary to use specialized results from differential algebra, especially Picard—Vessiot theory, the necessary definitions and theorems are supplied.FeaturesCollects the basic definitions and results about differential modules in one convenient reference with uniform notationAccessible to readers who don’t have extensive specialized knowledge of differential algebra or commutative ring theoryThe first book of its kind dedicated exclusively to the topic in this generalityPresents new formulations of previously published work as well as new results not previously published

"Presenting the proceedings of a conference held recently at Northwestern University, Evanston, Illinois, on the occasion of the retirement of noted mathematician Daniel Zelinsky, this novel reference provides up-to-date coverage of topics in commutative and noncommutative ring extensions, especially those involving issues of separability, Galois theory, and cohomology."