Pevzner, Alexandra2024-08-222024-08-222024-06https://hdl.handle.net/11299/265159University of Minnesota Ph.D. dissertation. June 2024. Major: Mathematics. Advisor: Victor Reiner. 1 computer file (PDF); viii, 56 pages.This thesis studies the fixed quotient of a commutative ring with group action, which is naturally a module over the ring of invariants. The perspective of graded syzygies is used to analyze the module structure. Chapter 4 concerns fixed quotients of polynomial rings, focusing on a stability pattern that emerges as the number of indeterminates increases. Chapter 5 studies a deformation of the polynomial ring, working towards a proof that the syzygies of the deformation's fixed quotient bound those of the polynomial ring.enThesis or Dissertation