691 research outputs found
Notes on Simple Modules over Leavitt Path Algebras
Given an arbitrary graph E and any field K, a new class of simple left
modules over the Leavitt path algebra L of the graph E over K is constructed by
using vertices that emit infinitely many edges. The corresponding annihilating
primitive ideals are described and is used to show that these new class of
simple L-modules are different from(that is non-isomorphic to) any of the
previously known simple modules. Using a Boolean subring of idempotents induced
by paths in E, bounds for the cardinality of the set of distinct isomorphism
classes of simple L-modules are given. We also append other information about
the Leavitt path algebra L(E) of a finite graph E over which every simple left
module is finitely presented.Comment: 17 page
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