Maximal orders and noetherian semigroupalgebras.

An important aim in the study of noethering rings is the construction of new classes of non-commutative finitely presented Noetherian algebras which share "good" algebraic and homological properties with commutative polynomial algebras. In this project we search for a classification of Noetherian semigroup algebras that are a maximal order. Further, we desire a description of the class group and thus also a description of the height one prime ideals. Special attention will be given to the finitely presented algebras that are defined via square free monomial quadatric homogeneous equations. Here we mainly apply combinatorial techniques. This way we obtain an important test class for the previously mentioned problem. Also, we obtain algebras which give solutions to the Yang-Baxter equation.