For readers with a basic graduate level background in algebra, these ten articles provide a readable introduction to three major interrelated subjects of noncommutative algebra. The theme is the interplay between group theory and ring theory, dealing specifically with group rings, crossed products, and the Galois theory of rings. The author has carefully included most definitions, to keep the required background minimal. Each article contains a selection of results on the given topic, a limited number of proofs or sketches, and at least a few open problems
This is a new text for the Abstract Algebra course. The author has written this text with a unique, yet historical, approach: solvability by radicals. This approach depends on a fields-first organization. However, professors wishing to commence their course with group theory will find that the Table of Contents is highly flexible, and contains a generous amount of group coverage.
College algebra has a basic unity. It should consist of, study of the number systems of elementary mathematics, olynomials and allied functions, algebraic identities, equaions, and systems of equations. The unity of the present ext is achieved by fitting the standard topics of college algebra into this pattern...
Local Cohomology: An Algebraic Introduction with Geometric ApplicationsThis book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and illustrates many applications for the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo-Mumford regularity, the Fulton-Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology.
This volume contains selected refereed papers based on lectures presented at the ´;Fifth International Fez Conference on Commutative Algebra and Applications´ that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
