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
相关论文
共 30 条
[1]   SEMISIMPLE ALGEBRAS OF INFINITE VALUED LOGIC AND BOLD FUZZY SET-THEORY [J].
BELLUCE, LP .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1986, 38 (06) :1356-1379
[2]  
Bergman GM., 2015, UNIVERSITEXT
[3]  
Blyth T. S., 2005, UNIVERSITEX
[4]   The stable topology for residuated lattices [J].
Busneag, Catalin ;
Piciu, Dana .
SOFT COMPUTING, 2012, 16 (10) :1639-1655
[5]  
Busneag D, 2021, CARPATHIAN J MATH, V37, P53
[6]  
Busneag D, 2015, J MULT-VALUED LOG S, V24, P529
[7]  
Cattaneo G, 2009, LECT NOTES COMPUT SC, V5656, P67, DOI 10.1007/978-3-642-03281-3_3
[8]  
Cornish W.H., 1973, J. Aust. Math. Soc., V15, P70
[9]  
Cretan R, 2006, ANN UNIV CRAIOVA-MAT, V33, P174
[10]  
Dong YY, 2019, SOFT COMPUT, V23, P3207, DOI 10.1007/s00500-018-3195-9
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