连通代数domain上相容紧元及范畴的研究

The Reasearch of Consistent Compact Element and Category on Connected Algebra Domain

基于连通集的定义,引入了c-理想的概念,得出了连通代数domain中每一个元都是相容紧元,当且仅当它的每个c-理想都是主c-理想,给出了连通代数domain满足升链条件。研究了连通完备偏序集A中的每个元是相容紧元的充要条件是A与A的c-理想格同构。最后,证明了连通代数domain范畴与偏序集范畴等价。

On the basis of the definition of connected set, the c-ideal was given. The conclusions were drawn that every element of connected algebraic domain is consistent compact if every c-ideal is a principal c-ideal, and connected algebraic domain satisfies the ascending chain condition. Secondly, every element of A is consistent compact iff A is isomorphic to c-ideal lattice of A on connected complete poset. It was proved that the category of connected algebraic domain is equivalent to that of posets.