الصفحة 1
الصفحة 1
Modules and Comodules
The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006 and dedicated to Robert Wisbauer on the occasion of his 65th birthday. These articles reflect Professor Wisbauer's wide interests and give an overview of different fields related to module theory, some of which have a long tradition whereas others have emerged in recent years. They include topics in the formal theory of modules bordering on category theory, in ring theory, in Hopf algebras and quantum groups, and in corings and comodules.
Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories
"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra
Algebraic Geometry is the study of systems of polynomial equations in one or more variables.The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.
