We generalize tilting 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. Our construction is motivated by the connection between tilting and derived categories. We develop a …
A previously unrecognized class of a priori indecomposable modules, containing all the commonly known indecomposable modules over an Artin ring, is studied. Modules in this class are termed modules with cores. Amalgamating modules with cores, other indecomposable modules, not ne…
This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field.
This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field. Beyond assuming some first-year graduate algebra and basic homological algebra, the presentation is entirely self-contained, so the b…