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中文摘要：
引进一个偏序集的代数完备，并且构造任意偏序集的一个代数完备。有最小元的并半格的代数完备正好是它的理想完备。一个偏序集的代数完备同构于它的一个由下集作为元的完备格，并且这个完备格包含所有主理想。基于代数完备的Galois联络的下扩张仍然是一个Galois联络。
英文摘要：
This paper introduces the notion of algebraic completion of a poset and constructs a concrete algebraic completion of a poset. An ideal completion of P is just an algebraic completion of P whenever P is a join semilattice with a bottom. An algebraic completion of a poser P could be represented by a down-set algebraic lattice which contains all principal ideals. The lower extension of a Galois connection is again a Galois connection based on algebraic completion.
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