A study of homological invariants modulo an exact zero divisor

Let Q be a commutative local ring and R a quotient ring of Q by an ideal generated by an exact zero divisor. We use differential graded structures to describe a construction that produces a minimal free resolution of an R-module from the free resolution of the same module, considered as a Q-module, and the free resolution of R as a Q-module. We provide an explicit algorithm for this construction, written for the computer algebra system Macaulay2. Given two R-modules, we then use a mapping cone construction to relate homology of the two modules over Q to homology over R, and we give applications of this construction to the study of several homological invariants, such as complexity, curvature and generalized Poincaré series.

Name thesis:degree_name

Ph.D. (Doctor of Philosophy)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics (UMKC)

Grantor

University of Missouri--Kansas City

Year dc:date.issued

2024

Author dc:creator

• Sireeshan, Deepak

Advisors dc:contributor.advisor

• Sega, Liana
• Uddin, Md Yusuf Sarwar (Mohammad Yusuf Sarwar)

Handle dc:identifier.uri

https://hdl.handle.net/10355/101625

OAI identifier oai:identifier

oai:mospace.umsystem.edu:10355/101625