α-Ideals in Bounded Commutative Residuated Lattices

被引：0

作者：

Kakeu, Ariane G. Tallee ^{[1
]}

Strungmann, Lutz ^{[2
]}

Njionou, Blaise B. Koguep ^{[1
]}

Lele, Celestin ^{[1
]}

机构：

[1] Univ Dschang, Fac Sci, Dept Math & Comp Sci, POB 67, Dschang, West Region, Cameroon

[2] Mannheim Univ Appl Sci, Fac Comp Sci, D-68163 Mannheim, Germany

来源：

NEW MATHEMATICS AND NATURAL COMPUTATION | 2023年 / 19卷 / 03期

关键词：

Bounded commutative residuated lattice; Heyting algebra; ideal; prime ideal; annihilator; alpha-ideal; CLOSURE OPERATORS; PRIME; ALGEBRAS; FILTERS; SPACES; LOGIC;

D O I：

10.1142/S1793005723500254

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This study aims to introduce the concept of alpha-ideal in bounded commutative residuated lattices and establish some related properties. In this paper, we show that the set of alpha-ideals of a bounded commutative residuated lattice is a Heyting algebra, and an algebraic lattice. Moreover, we state the prime alpha-ideal theorem, and describe relations between alpha-ideals and some types of ideals of a bounded commutative residuated lattice. Finally, we discuss correspondences between alpha-ideals and alpha-filters of a bounded commutative residuated lattice.

引用

页码：611 / 630

页数：20

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