Memoirs of the American Mathematical Society 1996; 88 pp; softcover Volume: 120 ISBN10: 0821804448 ISBN13: 9780821804445 List Price: US$44 Individual Members: US$26.40 Institutional Members: US$35.20 Order Code: MEMO/120/575
 In this book, the authors generalize with respect to a tilting module of projective dimension at most one for an artin algebra to tilting with respect to a torsion pair in an abelian category. A general theory is developed for such tilting and the reader is led to a generalization for tilted algebras which the authors call "quasitilted algebras". This class also contains the canonical algebras, and the authors show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. The authors also give other characterizations of quasitilted algebras and give methods for constructing such algebras. In particular, they investigate when onepoint extensions of hereditary algebras are quasitilted. Readership Graduate students and research mathematicians interested in associative rings and algebras. Table of Contents  Introduction
 Tilting in abelian categories
 Almost hereditary algebras
 One point extensions of quasitilted algebras
 Bibliography
 Index
