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Ideal Approximation Theory

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Furuzan Ozbek, University of Kentucky

What
  • Colloquium
When Apr 23, 2014 04:00 PM to
Apr 24, 2014 05:00 PM
Where Ritter Hall 29
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Abstract: In this talk we examine the theory of covering (enveloping) 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. The definition of cover and envelope by modules carry over to the ideals very 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 will 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 (where A_2 is the category of all representations of 2-quiver by R-modules) 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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