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.

Commutative rings graded by abelian groups

Brian P Johnson, University of Nebraska - Lincoln


Rings graded by [special characters omitted] and [special characters omitted] play a central role in algebraic geometry and commutative algebra, and the purpose of this thesis is to consider rings graded by any abelian group. A commutative ring is graded by an abelian group if the ring has a direct sum decomposition by additive subgroups of the ring indexed over the group, with the additional condition that multiplication in the ring is compatible with the group operation. In this thesis, we develop a theory of graded rings by defining analogues of familiar properties—such as chain conditions, dimension, and Cohen-Macaulayness. We then study the preservation of these properties when passing to gradings induced by quotients of the grading group.

Subject Area


Recommended Citation

Johnson, Brian P, "Commutative rings graded by abelian groups" (2012). ETD collection for University of Nebraska - Lincoln. AAI3519459.