Abstract
In this paper, we show the principal theorem, on the extension of a negative (or positive) plurisubharmonic (ie dd(c)T >= 0) current T with condition on the slice. First, We prove the Chern-Levine-Nirenberg inequality for a positive (or negative) psh current. The result generalized a result of Sibony and the results of Bedford-Taylor and Demailly for a positive d-closed current. Also we show a inequality of Oka type for a positive psh current.