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Computational Methods For Oi-Modules, Michael Morrow

Theses and Dissertations--Mathematics

Computational commutative algebra has become an increasingly popular area of research. Central to the theory is the notion of a Gröbner basis, which may be thought of as a nonlinear generalization of Gaussian elimination. In 2019, Nagel and Römer introduced FI- and OI-modules over FI- and OI-algebras, which provide a framework for studying sequences of related modules defined over sequences of related polynomial rings. In particular, they laid the foundations of a theory of Gröbner bases for certain classes of OI-modules. In this dissertation we develop an OI-analog of Buchberger's algorithm in order to compute such Gröbner bases, as well …