论文标题
平坦的拓扑，最大和最小的量子光谱
Flat topology on prime, maximal and minimal prime spectra of quantales
论文作者
论文摘要
可以在质数，最大和最小的质子光谱上定义几种拓扑。其中，我们提到了Zariski拓扑，贴片拓扑结构和扁平拓扑。通过使用这些拓扑结构，Tarizadeh和Aghajani最近获得了各种环的新特征：Gelfand Rings，Clean Rings，Bectine Flat Flating Rings，$ MP $ -MP $ - 戒指等。本文的目的是将其一些结果概括为量化，这些结构构成了理想，过滤器和一致性的晶格的良好抽象化。我们将在素数，最大和最小的质量光谱上研究平坦的拓扑和斑块拓扑。通过使用这两个拓扑结构，可以获得针对超烷量，正常量子，b normal量子，$ MP $ - 量子和$ pf $ - 量子的新定理定理。一般结果可以应用于几个混凝土代数：交换环，有界的分布晶格，MV代数，BL-Elgebras，残留的晶格，交换性Unital $ L $ - 组等。
Several topologies can be defined on the prime, the maximal and the minimal prime spectra of a commutative ring; among them, we mention the Zariski topology, the patch topology and the flat topology. By using these topologies, Tarizadeh and Aghajani obtained recently new characterizations of various classes of rings: Gelfand rings, clean rings, absolutely flat rings, $mp$ - rings,etc. The aim of this paper is to generalize some of their results to quantales, structures that constitute a good abstractization for lattices of ideals, filters and congruences. We shall study the flat and the patch topologies on the prime, the maximal and the minimal prime spectra of a coherent quantale. By using these two topologies one obtains new characterization theorems for hyperarchimedean quantales, normal quantales, B-normal quantales, $mp$ - quantales and $PF$ - quantales. The general results can be applied to several concrete algebras: commutative rings, bounded distributive lattices, MV-algebras, BL-algebras, residuated lattices, commutative unital $l$ - groups, etc.
