论文标题
MP溶液的晶格
Mp-residuated lattices
论文作者
论文摘要
本文致力于研究一类令人着迷的残留晶格，即所谓的MP救助晶格，其中任何原始滤波器都包含独特的最小质量滤波器。代数和拓扑方法的组合用于在MP验证的晶格上获得新的结构结果。已经证明，由双壳 - 内核拓扑与MP验证的晶格紧密相关。尤其是，当且仅当其最小的原始频谱（配备了双壳内亲属拓扑）的最小序列时，当时残留的晶格是MP，当时且仅当其质谱均配备了双壳核拓扑的序列时，才是正常的。 MP验证的晶格类的特征是纯过滤器的手段。结果表明，当且仅当其纯过滤器恰好是其最小的质量过滤器时，当且仅当其纯光谱与其最小的质子光谱同构时，其纯过滤器恰好是最小的质子过滤器，该晶格是MP。
This paper is devoted to the study of a fascinating class of residuated lattices, the so-called mp-residuated lattice, in which any prime filter contains a unique minimal prime filter. A combination of algebraic and topological methods is applied to obtain new and structural results on mp-residuated lattices. It is demonstrated that mp-residuated lattices are strongly tied up with the dual hull-kernel topology. Especially, it is shown that a residuated lattice is mp if and only if its minimal prime spectrum, equipped with the dual hull-kernel topology, is Hausdorff if and only if its prime spectrum, equipped with the dual hull-kernel topology, is normal. The class of mp-residuated lattices is characterized by means of pure filters. It is shown that a residuated lattice is mp if and only if its pure filters are precisely its minimal prime filters, if and only if its pure spectrum is homeomorphic to its minimal prime spectrum, equipped with the dual hull-kernel topology.
