Title:

Finiteness conditions on the Extalgebra

Let A be a finitedimensional algebra given by quiver and monomial relations. In [18] we see that the Extalgebra of A is finitely generated only if all the Extalgebras of certain cycle algebras overlying A are finitely generated. Here a cycle algebra Lambda is a finitedimensional algebra given by quiver and monomial relations where the quiver is an oriented cycle. The main result of this thesis gives necessary and sufficient conditions for the Extalgebra of such a Lambda to be finitely generated; this is achieved by defining a computable invariant of Lambda, the smotube. We also give necessary and sufficient conditions for the Extalgebra of Lambda to be Noetherian.;Let Lambda be a triangular matrix algebra, defined by algebras T and U and a TUbimodule M. Under certain conditions we show that if the Extalgebras of T and U are right (respectively left) Noetherian rings, then the Extalgebra of Lambda is a right (respectively left) Noetherian ring. An example shows the hypotheses used cannot be improved. We also specialise to the case where Lambda is a onepoint extension: we give a specific presentation of a result that parallels a similar theorem for the more general case above.
