Mathematical Sciences: Integral Representations and Ring Theory

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This research is concerned with the structure of modules, with emphasis on their direct-sum relations and local-global relations. The class of rings involved is that of module-finite algebras over a commutative noetherian ring of Krull dimension 1. The object is to remove the traditional restrictions on the algebra and obtain new results in integral representation theory. A ring is an algebraic object having an addition and multiplication defined on it. The most familiar example is the ring of integers. These objects occur in many different settings in mathematics and theoretical physics.