This research is concerned with the representation theory of algebras. The principal investigator will examine the homological properties of the class of Artin algebras by examining the relationship between certain exact sequences and the homomorphisms of one module into another. In addition, the structure of projective resolutions of modules over Artinian rings will be studied. It has been shown that a resolution for an arbitrary finitely generated simple module over an Artin algebra, finite dimensional over an algegraically closed field, can be obtained algorithmically. This approach will be extended to more general situations.
