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
收藏
页码：611 / 630
页数：20
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