文章借助格理论中的素元与余素元的定义，通过对偏序集上内部算子和闭包算子的研究，提出了素内部算子与素闭包算子的定义，讨论了它们与内部算子和闭包算子之间的联系，得到了相应的等价刻画，进一步丰富了偏序集上的算子理论。%In this paper, we firstly give a new definitions of the prime inner operator and prime closure operator through combining the definitions of prime element, co- prime element and inner operator , closure operator respectively, and then discuss the relation between the prime inner（closure） operator and the inner（closure） operator. Also some equivalent characterizations are obtained which generalize the operator theory further.
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