Mathematics, Department of


First Advisor

Tom Marley

Date of this Version



Funk,T.H. (2021). Frobenius and Homological Dimensions of Complexes [Doctoral dissertation, University of Nebraska - Lincoln]. ProQuest Dissertations and Theses database.


A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Tom Marley. Lincoln, Nebraska: May, 2021

Copyright © 2021 Taran Funk


Much work has been done showing how one can use a commutative Noetherian local ring R of prime characteristic, viewed as algebra over itself via the Frobenius endomorphism, as a test for flatness or projectivity of a finitely generated module M over R. Work on this dates back to the famous results of Peskine and Szpiro and also that of Kunz. Here I discuss what work has been done to push this theory into modules which are not necessarily finitely generated, and display my work done to weaken the assumptions needed to obtain these results.

Adviser: Tom Marley

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Algebra Commons