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On the Ideal Theory of Leavitt Path Algebras

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K. M. Rangaswamy, University of Colorado

What
  • Algebra Seminar
When Thu, Oct 20, 2016
from 11:00 AM to 11:50 AM
Where Ritter Hall 202
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ABSTRACT: Let E be an arbitrary directed  graph and let L be the Leavitt path algebra of the graph E over a field K. L admits three structures: L is a K-algebra, L is a graded ring and  L is also a ring with involution. These intermingling structures together the graphical properties of E yield interesting results about L and help in constructing interesting examples. Even though L is highly non-commutative, the ideals of L share a number of properties of ideals of commutative rings. We will show that the ideal multiplication in L is commutative. L can be considered as a non-commutative analogue of Prufer domains in the sense that the ideals of L form a distributive lattice and finitely generated one sided ideals of L are projective. L is shown to be a multiplication ring. Finally, existence and uniqueness of  factorizing of an ideal A of L as a product of finitely many prime, primary and/or irreducible ideals is explored. Examples will be constructed to illustrate the results and concepts.
 
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