Mathematical Sciences: Topics in Commutative Algebra

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Heinzer 9622224 This proposal supports the work of Professor W. Heinzer to work on problems in commutative algebra. He intends to study intermediate rings between a local domain and its completion. He also intends to study the structure of ideals in a two dimensional regular local ring, the ramification of prime ideals in infinite integral extensions, the contraction of ideals from one dimensional overrings with applications to primary decomposition in powers of ideals in Noetherian rings, and the content of Gaussian polynomials. This research is on the boundary between commutative algebra and algebraic geometry. Both fields arose from the classical problem of studying mathematical objects defined in the plane by the simplest of equations, namely polynomials. Today, the fields use methods not only from algebra, but also from analysis and topology, and conversely are extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.