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中文摘要：
引入了预格和预格同态的概念，研究了预格同态与序同态的关系，得到了预格同态是序同态的结论，并给出了预格同构的等价刻画，证明了预格间的映射是预格同构当且仅当它是序同构．定义了预格的强理想与强滤子，研究了其性质，讨论了预格与理想及滤子的联系和区别．基于强理想的概念，引入了强并不可约元、强余素元等概念，讨论了其与并不可约元、余素元的关系．
英文摘要：
Prelattice and prelattice homomorphisms are introduced, and the relation ot prelattice homomorphism and order homomorphism is studied. It is proved that a prelattice homomorphism is an order homomorphism. Moreover, an equivalent characterization of prelattice isomorphism is given, it is shown that a mapping between two prelattices is a prelattice isomorphism if and only if it is an order isomorphism. Strong ideal and strong filter on prelattice are defined, and the relation of ideal （resp. filter） and strong ideal （resp. strong filter） is studied. Based on strong ideal, strong join irreducible element and strong coprime element are defined and the relation of strong join irreducible element, strong coprime element, join irreducible element and coprime element is studied.
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