| Summary: | Graph can be represented into a path algebra over field K by adding two
axioms, denoteds by KE. If the graph is extended and added by axioms CK1 and
CK2, then can be defined Leavitt path algebra that is denoted by L(E). In fact, KE
is a sub algebra of L(E). Leavitt path algebra is � -graded algebra which graded
ideals are generated by hereditery and saturated subset of vertex set in graph.
Futhermore, through isomorphism of K-algebra, this ideals are Leavitt path
algebra too. By the simple properties of elemen of Leavitt path algebra, that are
elemens that contains only real path or ghost path, can be found term of graph to
define simple Leavitt path algebra.
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