Mathematical Sciences: Applications of Infinite Power SeriesType Skew Fields

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This project will examine the so called Freiheitssatz for noncommutative associative algebras, which states that for any non trivial relation there exists a nontrivial algebra with generators satisfying this relation. The principal investigator will also investigate the structure of skew fields which are infinite dimensional over their centers concentrating primarily on the search of free subobjects in such skew fields. A ring is an algebraic object having defined on it both an addition and a multiplication. These objects occur frequently in many branches of mathematics. They are also of interest in physics and computer science. This project will examine several constructions in order to answer some fundamental questions concerning the existence of rings with certain properties.