Date of Award
12-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Dr. Jim Coykendall
Committee Member
Dr. Srikanth Iyengar
Committee Member
Dr. Svetlana Poznanovikj
Committee Member
Dr. Michael Burr
Committee Member
Dr. Hui Xue
Abstract
This thesis is comprised of three chapters. The first chapter deals with a purely algebraic proof of a deep result of Quillen stating that the category of simplicial commutative algebras over a commutative ring is a model category. The central focus of our approach is on the study of shuffle product of connective chain complexes that provides a bridge to translate the constructions in the simplicial algebra world to the chain complex world.
The second chapter delves into Quillen's fundamental spectral sequences that relate Andre-Quillen homology and cohomology to Tor and Ext functors. Our comprehensive treatment develops and streamlines the requisite background constructions to provide a suitable framework in order to establish complete proofs.
The third chapter studies certain special classes of ring homomorphisms, the so-called complete intersection maps and exceptional complete intersection maps. Some research has been conducted to characterize or detect the exceptional property. We investigate this property further and discover new conditions to detect it.
Recommended Citation
Faridian, Hossein, "Andre-Quillen Homology and Special Classes of Ring Homomorphisms" (2024). All Dissertations. 3853.
https://open.clemson.edu/all_dissertations/3853
