Term of Award
Spring 2019
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Alina Iacob
Committee Member 1
Paul Sobaje
Committee Member 2
Jimmy Dillies
Abstract
We consider the following question: when is every exact complex of injective modules a totally acyclic one? It is known, for example, that over a commutative Noetherian ring of finite Krull dimension this condition is equivalent with the ring being Iwanaga-Gorenstein. We give equivalent characterizations of the condition that every exact complex of injective modules (over arbitrary rings) is totally acyclic. We also give a dual result giving equivalent characterizations of the condition that every exact complex of flat modules is F-totally acyclic over an arbitrary ring.
OCLC Number
1103526799
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/1fi10pa/alma9916223171002950
Recommended Citation
Zolt, Holly M., "Totally Acyclic Complexes" (2019). Electronic Theses and Dissertations. 1905.
https://digitalcommons.georgiasouthern.edu/etd/1905
Research Data and Supplementary Material
No
