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Dissertation Defense

Date:
-
Location:
318 Patterson Office Tower
Speaker(s) / Presenter(s):
Furuzan Ozbek, University of Kentucky

Title:  Subfunctors of Extension Functors

Abstract:  In this talk we examine subfunctors of Ext relative to covering (enveloping) classes and the theory of covering (enevloping) ideals. The notion of covers and envelopes by modules was introduced independently by Auslander-Smalo and Enochs and has proven to be beneficial for module theory as well as for representation theory. First we will focus on subfunctors of Ext and their properties. We show how the class of precoverings give us subfunctors of Ext. Later, we investigate the sunfunctor of Hom called ideals. The definition of cover and envelope carry over to the ideals naturally. Classical conditions for existence theorems for covers led to similar approaches in the ideal case. Even though some theorems such as Salce's Lemma were proven to extend  to ideals, most of the theorems do not directly apply to the new case. We show how Eklof-Trlifaj's result can partially be extended to the ideals generated by a set. Moreover by relating the existence theorems for covering ideals of morphisms by identifying the morphisms with objects in A_2 we obtain a sufficient condition for the existence of covering ideals in a more general setting and finish with applying this result to the class of phantom morphisms.

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