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Informationen zum Autor Giandomenico Boffi, a graduate of the Università "La Sapienza" (Roma), received his Ph.D. from Brandeis University (Waltham, MA). He is currently Professor of Algebra at the Università "G. d'Annunzio" (Chieti-Pescara). He has published articles on commutative algebra and representation theory.; David A. Buchsbaum, a graduate of Columbia College (New York), received his Ph. D. from Columbia University. He is Professor Emeritus of Mathematics at Brandeis University (Waltham, MA). His publications include articles on category theory, commutative algebra, homological algebra and representation theory as well as a graduate text in algebra. He was also an algebra editor for the Transactions of the Amer. Math. Soc. and a founding editor of the Journal of Algebra. A recipient of a Guggenheim Fellowship, he is also a fellow of the American Academy of Arts and Sciences. Klappentext Threading Homology through Algebra takes homological themes (Koszul complexes and their variations, resolutions in general) and shows how these affect the perception of certain problems in selected parts of algebra, as well as their success in solving a number of them. The text deals with regular local rings, depth-sensitive complexes, finite free resolutions, letter-place algebra, Schur and Weyl modules, Weyl-Schur complexes and determinantal ideals. Aimed at graduates and academics in mathematics, the book provides an overview of the developments that have taken place in these areas as well as an insight into some of the open problems which exist. Zusammenfassung Aimed at graduate students and researchers in mathematics, this book takes homological themes, such as Koszul complexes and their generalizations, and shows how these can be used to clarify certain problems in selected parts of algebra, as well as their success in solving a number of them. Inhaltsverzeichnis Preface 1: Recollections and perspectives 2: Local ring theory 3: Generalized Koszul complexes 4: Structure theorems for finite free resolutions 5: Exactness criteria at work 6: Weyl and Schur modules 7: Some applications of Weyl and Schur modules Appendix for letter-place methods References Index ...
