论文标题
Gelfand残留的晶格
Gelfand residuated lattices
论文作者
论文摘要
在本文中，使用代数和拓扑方法的组合来获得Gelfand残留的晶格的新结构结果。事实证明，Gelfand的残留晶格与船体内核拓扑密切相关。尤其是，当且仅当其配备船体内核拓扑的质谱是正常的情况下，且仅当它的质谱是正常的。引入了一类软残留的晶格，并且仅当它是gelfand和semisimple时，残留的晶格是柔软的。 Gelfand残留的晶格是使用过滤器的纯部分来表征的。描述了Gelfand残留的晶格中纯过滤器与自由基之间的关系。结果表明，当且仅当其纯谱与通常的最大光谱同构时，残留的晶格是Gelfand。表征了Gelfand残留的晶格的纯过滤器。最后，只有当且仅当赫尔 - 内尔内尔和$ \ mathscr {d} $ - 拓扑结合在最大过滤器的集合上时，就证明了残留的晶格是Gelfand。
In this paper, a combination of algebraic and topological methods is applied to obtain new and structural results on Gelfand residuated lattices. It is demonstrated that Gelfand's residuated lattices strongly tied up with the hull-kernel topology. Especially, it is shown that a residuated lattice is Gelfand if and only if its prime spectrum, equipped with the hull-kernel topology, is normal. The class of soft residuated lattices is introduced, and it is shown that a residuated lattice is soft if and only if it is Gelfand and semisimple. Gelfand residuated lattices are characterized using the pure part of filters. The relation between pure filters and radicals in a Gelfand residuated lattice is described. It is shown that a residuated lattice is Gelfand if and only if its pure spectrum is homeomorphic to its usual maximal spectrum. The pure filters of a Gelfand residuated lattice are characterized. Finally, it is proved that a residuated lattice is Gelfand if and only if the hull-kernel and the $\mathscr{D}$-topology coincide on the set of maximal filters.
