Ultra LI-ideals in lattice implication algebras and MTL-algebras

被引：1
|
作者：
Xiaohong Zhang
Keyun Qin
Wiesław A. Dudek
机构：
[1] Ningbo University,Department of Mathematics, Faculty of Science
[2] Southwest Jiaotong University,Department of Applied Mathematics
[3] Wrocław University of Technology,Institute of Mathematics and Computer Science
来源：
Czechoslovak Mathematical Journal | 2007年 / 57卷
关键词：
lattice implication algebra; -algebra; (prime, ultra, obstinate, Boolean) ; -ideal; -ideal;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A mistake concerning the ultra LI-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an LI-ideal to be an ultra LI-ideal are given. Moreover, the notion of an LI-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) LI-ideal and an ILI-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper LI-ideal and Boolean LI-ideal, (2) prime proper LI-ideal and ILI-ideal, (3) proper obstinate LI-ideal, (4) ultra LI-ideal.
引用
收藏
页码：591 / 605
页数：14
相关论文
共 45 条
  • [1] Ultra LI-ideals in lattice implication algebras and MTL-algebras
    Zhang, Xiaohong
    Qin, Keyun
    Dudek, Wieslaw A.
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2007, 57 (02) : 591 - 605
  • [2] Ultra LI-ideals in lattice implication algebras
    Keyun Qin
    Yang Xu
    Young Bae Jun
    Czechoslovak Mathematical Journal, 2002, 52 : 463 - 468
  • [3] Ultra LI-ideals in lattice implication algebras
    Qin, KY
    Xu, Y
    Jun, YB
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2002, 52 (03) : 463 - 468
  • [4] Neutrosophic LI-ideals in lattice implication algebras
    Borzooei, Rajab Ali
    Kish, Mandi Sabet
    Jun, Y. B.
    NEUTROSOPHIC SETS AND SYSTEMS, 2019, 31 : 282 - 296
  • [5] On Intuitionistic Fuzzy LI-ideals in Lattice Implication Algebras
    Chunhui LIU
    JournalofMathematicalResearchwithApplications, 2015, 35 (04) : 355 - 367
  • [6] Strong prime LI-ideals in lattice implication algebras
    Bai, Lijun
    Xu, Yang
    Chang, Zhiyan
    Xu, Weitao
    PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON INTELLIGENT SYSTEMS AND KNOWLEDGE ENGINEERING (ISKE 2007), 2007,
  • [7] (∈,∈ Vq)-fuzzy LI-ideals in lattice implication algebras
    Peng, Jiayin
    Lecture Notes in Electrical Engineering, 2012, 135 LNEE : 221 - 226
  • [8] ILI-ideals and prime LI-ideals in lattice implication algebras
    Liu, YL
    Liu, SY
    Xu, Y
    Qin, KY
    INFORMATION SCIENCES, 2003, 155 (1-2) : 157 - 175
  • [9] Lattice of Interval-Valued (∈,∈∨q)-Fuzzy LI-Ideals in Lattice Implication Algebras
    Chunhui LIU
    JournalofMathematicalResearchwithApplications, 2016, 36 (04) : 394 - 406
  • [10] Interval-Valued Intuitionistic (T, S)-Fuzzy LI-Ideals in Lattice Implication Algebras
    Liu, Chun-Hui
    QUANTITATIVE LOGIC AND SOFT COMPUTING 2016, 2017, 510 : 337 - 347
12345