This award supports research in commutative algebra and ring theory. One of the principal investigators will work on the integral representation of Gl(n). The other principal investigator will work on the representation theory of artin algebras and theory of lattices over higher dimensional orders, with special emphasis on maximal Cohen-Macaulay modules over isolated Cohen-Macaulay singularities. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication defined on it. Although the additive operation satisfies the commutative law, the multiplicative operation is not required to do so. An example of a ring for which multiplication is not commutative is the collection of nxn matrices over the integers. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.
