Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences



First Advisor

Dr. Uwe Nagel


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 as an OI-analog of Schreyer's theorem to compute their modules of syzygies. We also give an application of our results to the computation of free OI-resolutions, and showcase our Macaulay2 package "OIGroebnerBases.m2'' which implements these constructions. Lastly, we show how our results can be tweaked to compute free FI-resolutions.

Digital Object Identifier (DOI)

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Algebra Commons