Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.

Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.

Characterizations of Gorenstein Rings Using Frobenius

Brittney Falahola, University of Nebraska - Lincoln

Abstract

Let R be a local commutative Noetherian ring of characteristic p > 0 and f : R R the Frobenius ring homomorphism sending r R to its pth power rp. Denote by Rf the R – R-bimodule with additive group R and left and right R-actions given by r·u = ru and u·r = urp for all r R, uRf. The Frobenius functor FR takes a left R-module M to the left R-module FR( M) := RfRM. Motivated by work of Peskine and Szpiro, Marley, and Webb, we give various characterizations of Gorenstein local rings of prime characteristic through investigations into how the Frobenius functor interacts with injective dimension, injective resolutions, and certain Tor modules.^ We also include separate work, in the setting of commutative Noetherian rings (with no prime characteristic assumption), which establishes when certain maps in the direct limit definition of local cohomology are injective. ^

Subject Area

Mathematics|Theoretical mathematics

Recommended Citation

Falahola, Brittney, "Characterizations of Gorenstein Rings Using Frobenius" (2017). ETD collection for University of Nebraska - Lincoln. AAI10272020.
http://digitalcommons.unl.edu/dissertations/AAI10272020

Share

COinS