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.

Cohen-Macaulay dimension for coherent rings

Rebecca Egg, University of Nebraska - Lincoln


This dissertation presents a homological dimension notion of Cohen-Macaulay for non-Noetherian rings which reduces to the standard definition in the case that the ring is Noetherian, and is inspired by the homological notion of Cohen-Macaulay for local rings developed by Gerko. Under this notion, both coherent regular rings (as defined by Bertin) and coherent Gorenstein rings (as defined by Hummel and Marley) are Cohen-Macaulay. This work is motivated by Glaz's question regarding whether a notion of Cohen-Macaulay exists for coherent rings which satisfies certain properties and agrees with the usual notion when the ring is Noetherian. Hamilton and Marley gave one answer; we develop an alternative approach using homological dimensions which seems to have more satisfactory properties. We explore properties of coherent Cohen-Macaulay rings, as well as their relationship to non-Noetherian Cohen-Macaulay rings as defined by Hamilton and Marley.

Subject Area


Recommended Citation

Egg, Rebecca, "Cohen-Macaulay dimension for coherent rings" (2016). ETD collection for University of Nebraska-Lincoln. AAI10128766.