Scholarlink

<p>This paper is concerned with the properties of the prime spectrum of MV-algebras, namely the space of its prime ideals with the Zariski topology which is an important topological invariant of MV-algebras. The prime spectrum is a complete invariant in Boolean algebras, but in MV-algebras this is not the case. Nevertheless knowledge of the prime spectrum gives a lot of information: There are many properties of MV-algebras which depend only on the spectrum. We call these properties “topological” and we study them. For instance, we prove that simplicity and strong simplicity are topological as well as the class of hyperarchimedean MV-algebras and the class of regular MV-algebras, while the class of perfect MV-algebras and algebraically closed are not.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Topological Classes of MV-Algebras

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月26日

查看全文
  • Giuseppina Barbieri,
  • Antonio Di Nola,
  • Giacomo Lenzi

摘要

This paper is concerned with the properties of the prime spectrum of MV-algebras, namely the space of its prime ideals with the Zariski topology which is an important topological invariant of MV-algebras. The prime spectrum is a complete invariant in Boolean algebras, but in MV-algebras this is not the case. Nevertheless knowledge of the prime spectrum gives a lot of information: There are many properties of MV-algebras which depend only on the spectrum. We call these properties “topological” and we study them. For instance, we prove that simplicity and strong simplicity are topological as well as the class of hyperarchimedean MV-algebras and the class of regular MV-algebras, while the class of perfect MV-algebras and algebraically closed are not.