论文标题
网状函数和转移属性
Reticulation functor and the transfer properties
论文作者
论文摘要
众所周知，通过使用换向器操作，对于每个一致性模块化代数$ a $一个人都可以定义一个素数的概念。 $ a $的Prime一致性的集合$ SPEC（a）$具有Zariski风格的拓扑结构。代数$ a $的网状是一个有界的分布晶格$ l（a）$，其Prime Spectrum $ spec（l（a））$（带有石材拓扑结构）是自杀到$ spec（a）$的。 在最近的一篇论文中，C.Mureşan和作者证明了Semidegerenter Goldence Modular Modular代数$ a $的网状存在。 本文旨在对两种类型的问题做出答案： $（i）$如何将代数$ a $的某些属性转移到晶格$ l（a）$和viceversa，如何将$ l（a）$的某些属性转移到$ a $中； $（ii）$如何使用$（i）$的转移属性来证明一些非凡的代数类别的一些新旧特征。 我们研究了与布尔中心，歼灭者，补丁和平面拓扑，Pierce Spectrum，Pure和$ w $ - 纯的一致性，运营商$ KER（\ cdot）$和$ O（\ cdot）$等相关的转移属性。 通过使用这些转移属性，我们获得了几种代数的表征定理：hyparchimedean代数，一致性正常和一致性$ b $ - 普通代数，$ MP $ - 代数 - 代数，$ PF $ - 代数，代数，一致性纯化代数和$ PP $ - Algebras。
It is known that by using the commutator operation, for each congruence modular algebra $A$ one can define a notion of prime congruence. The set $Spec(A)$ of prime congruences of $A$ is endowed with a Zariski style topology. The reticulation of the algebra $A$ is a bounded distributive lattice $L(A)$ whose prime spectrum $Spec(L(A))$ (with the Stone topology) is homemorphic to $Spec(A)$. In a recent paper, C. Mureşan and the author have proven the existence of reticulation for a semidegenerate congruence modular algebra $A$. The present paper aims to give an answer to two types of problems: $(I)$ how some properties of the algebra $A$ can be transferred to the lattice $L(A)$ and viceversa, how some properties of $L(A)$ can be transferred to $A$; $(II)$ how the transfer properties from $(I)$ can be used to prove some old and new characterizations of some remarkable classes of algebras. We study the transfer properties related to Boolean centers, annihilators, patch and flat topologies of spectra, Pierce spectrum, pure and $w$ - pure congruences, the operators $Ker(\cdot)$ and $O(\cdot)$,etc. By using these transfer properties, we obtain characterization theorems for several types of algebras : hyperarchimedean algebras, congruence normal and congruence $B$ - normal algebras, $mp$ - algebras, $PF$ - algebras, congruence purified algebras and $PP$ - algebras.
