Monadic $k\times j$-rough Heyting algebras

IF 0.3 4区数学 Q1 Arts and Humanities Archive for Mathematical Logic Pub Date : 2021-11-13 DOI:10.1007/s00153-021-00802-6

Federico Almiñana, Gustavo Pelaitay

引用次数: 3

Abstract

In this paper, we introduce the variety of algebras, which we call monadic $k\times j$-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in $3\times 2$ case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic $k\times j$-rough Heyting algebras. In order to this, an Esakia-style duality for these algebras is developed.

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一元$k\times j$ -粗糙的Heyting代数

在本文中，我们引入了代数的多样性，我们称之为单元\（k \ times j \）-粗糙Heyting代数。这些代数构成了一元Heyting代数的扩展，并且在\（3\times2\）的情况下，它们与一元3值的Łukasiewicz–Moisil代数重合。我们的主要兴趣是简单和次直不可约的一元\（k\timesj\）-粗糙Heyting代数的刻画。为此，发展了这些代数的Esakia型对偶。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.

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Monadic \(k\times j\)-rough Heyting algebras

Abstract