论文标题
残留的晶格的纯光谱
The pure spectrum of a residuated lattice
论文作者
论文摘要
本文研究了所谓的纯过滤器中残留的晶格中一种引人入胜的过滤器。在残留晶格的纯过滤器上使用代数和拓扑方法的组合，以获得一些新的结构结果。已经研究了残留晶格的纯prime滤波器的概念，并获得了Cohen型定理。结果表明，残留的晶格的纯光谱是一个紧凑的清醒空间，并且已经证明了斜体型定理。事实证明，Gelfand残留的晶格的纯光谱是Hausdorff空间，并推断出Gelfand残留的晶格的纯光谱与通常的最大光谱同构。最后，研究了由MP溶液的晶格的纯光谱，并证实了给定的残基晶格是MP，如果其最小的质谱均配备了诱导的双壳源拓扑，并且其纯谱是相同的。
This paper studies a fascinating type of filter in residuated lattices, the so-called pure filters. A combination of algebraic and topological methods on the pure filters of a residuated lattice is applied to obtain some new structural results. The notion of purely-prime filters of a residuated lattice has been investigated, and a Cohen-type theorem has been obtained. It is shown that the pure spectrum of a residuated lattice is a compact sober space, and a Grothendieck-type theorem has been demonstrated. It is proved that the pure spectrum of a Gelfand residuated lattice is a Hausdorff space, and deduced that the pure spectrum of a Gelfand residuated lattice is homeomorphic to its usual maximal spectrum. Finally, the pure spectrum of an mp-residuated lattice is investigated and verified that a given residuated lattice is mp iff its minimal prime spectrum is equipped with the induced dual hull-kernel topology, and its pure spectrum is the same.
