Gorenstein Injective Modules under Flat Base Change

James Gossell – Clemson University

Abstract: Let A be a commutative noetherian ring and M an A-module. The injective dimension of M gives a measurement of how badly M fails to be an injective module. In 1975, Hans-Bjorn Foxby introduced a technique to determine the injective dimension of any flat base change of an injective module. This technique can be used to verify that injective modules remain injective under certain flat base changes, such as a localization. In this talk we will discuss this technique and preview future research on a possible extension of Foxby’s result for Gorenstein injective modules.