Hammocks for String Algebras

this paper we consider the class of string algebras and deal with the corresponding problem. These algebras are usually representation-infinite and are regarded as an important class of tame algebras. We introduce a generalized notion of hammocks for string algebras and prove various combinatorial properties of these posets. In case one is dealing with a representation-finite string algebra, our definition and the definition given in [RV] coincide. As a main application we compute the index of nilpotency (up to a small error term) of the radical of A-mod where A is a string algebra. We also construct examples which show that every possible index occurs. Only very few examples of this type were known before