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 50 条
  • [41] σ-Ideals in distributive pseudocomplemented residuated lattices
    Celani, Sergio A.
    SOFT COMPUTING, 2015, 19 (07) : 1773 - 1777
  • [42] Ideals and Bosbach States on Residuated Lattices
    Woumfo, Francis
    Koguep Njionou, Blaise B.
    Temgoua Alomo, Etienne R.
    Lele, Celestin
    NEW MATHEMATICS AND NATURAL COMPUTATION, 2021, 17 (02) : 281 - 302
  • [43] Almost minimal varieties of commutative residuated lattices
    Agliano, Paolo
    Galatos, Nikolaos
    Marcos, Miguel Andres
    INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2024, 34 (05) : 807 - 836
  • [44] Compatible operations on commutative weak residuated lattices
    Hernán Javier San Martín
    Algebra universalis, 2015, 73 : 143 - 155
  • [45] Minimal Varieties of Representable Commutative Residuated Lattices
    Rostislav Horčík
    Studia Logica, 2012, 100 : 1063 - 1078
  • [46] Compatible operations on commutative weak residuated lattices
    Javier San Martin, Hernan
    ALGEBRA UNIVERSALIS, 2015, 73 (02) : 143 - 155
  • [47] FUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE RESIDUATED LATTICES
    Ghorbani, S.
    Hasankhani, A.
    IRANIAN JOURNAL OF FUZZY SYSTEMS, 2010, 7 (02): : 41 - 54
  • [48] The Structure of Semiconic Idempotent Commutative Residuated Lattices
    Chen, Wei
    MATHEMATICS, 2024, 12 (02)
  • [49] FREE REPRESENTABLE IDEMPOTENT COMMUTATIVE RESIDUATED LATTICES
    Olson, Jeffrey S.
    INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2008, 18 (08) : 1365 - 1394
  • [50] COMMUTATIVE SEMIRINGS AND THEIR LATTICES OF IDEALS
    ALARCON, FE
    ANDERSON, DD
    HOUSTON JOURNAL OF MATHEMATICS, 1994, 20 (04): : 571 - 590
12345