论文标题
测试准代数
Reticulation of Quasi-commutative Algebras
论文作者
论文摘要
一致性模数$ \ MATHCAL {V} $中的换向器操作使我们能够定义\ Mathcal {V} $和Prime Spectrum $ Spec（a）$ a $ a $的任何代数$ a \ in \ MATHCAL {V} $的素数。该频谱的首次系统研究可以在Agliano的论文中找到，该论文发表在《通用代数》（1993年）中。 \ Mathcal {V} $的代数$ a \的网状是有界的分布代数$ l（a）$，其质谱（赋予石材拓扑结构）是同型对$ spec（a）$的同型（由Agliano定义的拓扑）。在最近的一篇论文中，C.Mureşan和作者定义了半代数的代数$ a $ a $ a $ a $ a $ a $ a $ a $ $ \ mathcal {v} $，满足假设$（h）$：set $ k（a）$ a $ a $ a $ a $ a $ a $ a $ a $的$ a $是$ a $ a $的封闭者。该理论不涵盖非交通环的贝尔斯网状。在本文中，我们将在半代的一致性模块化$ \ Mathcal {V} $中介绍准共同代数，作为Belluce Quasi-cosi-commutative Cond的概括。我们定义并研究了准共同代数的网状概念，以便可以作为特定情况获得准共同环的钟形网状。我们证明了通过网状的标准代数和某些转移属性的特征定理
The commutator operation in a congruence-modular variety $\mathcal{V}$ allows us to define the prime congruences of any algebra $A\in \mathcal{V}$ and the prime spectrum $Spec(A)$ of $A$. The first systematic study of this spectrum can be found in a paper by Agliano, published in Universal Algebra (1993). The reticulation of an algebra $A\in \mathcal{V}$ is a bounded distributive algebra $L(A)$, whose prime spectrum (endowed with the Stone topology) is homeomorphic to $Spec(A)$ (endowed with the topology defined by Agliano). In a recent paper, C. Mureşan and the author defined the reticulation for the algebras $A$ in a semidegenerate congruence-modular variety $\mathcal{V}$, satisfying the hypothesis $(H)$: the set $K(A)$ of compact congruences of $A$ is closed under commutators. This theory does not cover the Belluce reticulation for non-commutative rings. In this paper we shall introduce the quasi-commutative algebras in a semidegenerate congruence-modular variety $\mathcal{V}$ as a generalization of the Belluce quasi-commutative rings. We define and study a notion of reticulation for the quasi-commutative algebras such that the Belluce reticulation for the quasi-commutative rings can be obtained as a particular case. We prove a characterization theorem for the quasi-commutative algebras and some transfer properties by means of the reticulation
