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Let E be an arbitrary graph and K be any field. For every non-graded ideal Iof the Leavitt path algebra L_{K}(E), we give an explicit description of thegenerators of I. Using this, we show that every finitely generated ideal ofL_{K}(E) must be principal. In particular, if E is a finite graph, then everyideal of L_{K}(E) must be principal ideal.

Every finitely generated ideal of a Leavitt path algebra is a principal ideal