Mathematical Sciences: Primary Decompositions and Ajoints of Ideals

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Swanson 96-23085 This proposal supports the work of Professor I. Swanson to work on problems in commutative algebra. She intends to study how, in Noetherian rings of prime characteristic, primary deomposiiton varies with Frobenius powers. She also hopes to develop algorithms for calculating adjoints and cores when the ring is not two dimensional. 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.