COSAM » Events » 2016 » November » Algebra Linear Algebra Seminar

 Algebra/Linear Algebra Seminar Time: Nov 01, 2016 (04:00 PM) Location: Parker Hall 224 Details: Speaker: Furuzan Ozbek Title: Generalized Baer's Criterion Abstract: In 1940, Baer proved that an $$R$$-module $$M$$ is injective if and only if any homomorphism from an ideal $$I$$ to $$M$$ can be extended to a homomorphism from the ring $$R$$ to $$M$$. In relative homological algebra, we define an analogous notion to injective modules which is called a Gorenstein Injective module. It is not difficult to see that every injective module is Gorenstein injective. Our goal has been to find a similar criterion to that of Baer's for the Gorenstein injectives. Our starting point was to look at a simple case where $$R$$ is a local, Gorenstein ring where $$dim R=1$$. Then we proved that M is Gorenstein injective if and only if $$Ext^1(R/,M)=0$$ for all $$R$$-regular elements $$r$$. We want to generalize this result to $$n$$-dimensional Gorenstein rings.

Last updated: 10/28/2016