JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (2): 9-13.doi: 10.6040/j.issn.1671-9352.0.2023.132

Previous Articles    

Relatively maximal ideals of co-residuated lattices

ZHANG Yaning, YAO Wei*   

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
  • Published:2025-02-14

PDF (PC)

12

Abstract: A concept of relatively maximal ideals of co-residuated lattices is introduced, and the properties and the relationships among relatively maximal ideals, prime ideals and ideals are studied. A sufficient condition of the ideal lattice of a co-residuated lattice to be a spatial frame is obtained.

Key words: co-residuated lattice, relatively maximal ideal, ideal lattice, spatial frame

CLC Number: 

  • O153.1
[1] 郑慕聪. 余剩余格及其应用[D]. 西安:陕西师范大学,2005. ZHENG Mucong. Co-residuated lattices with applications[D]. Xian: Shaanxi Normal University, 2005.
[2] 郑慕聪,王国俊. 余剩余格及其应用[J]. 模糊系统与数学,2005,19(4):7-12. ZHENG Mucong, WANG Guojun. Co-residuated lattice and application[J]. Fuzzy Systems and Mathematics, 2005, 19(4): 7-12.
[3] OH Ju Mok, KIM Yong Chan. Approximation operators and fuzzy rough sets in coresiduated lattices[J]. Korean Journal of Mathematics, 2021, 29(1):81-89.
[4] OH Ju Mok, KIM Yong Chan. Various fuzzy connections and fuzzy concepts in complete co-residuated lattices[J]. International Journal of Approximate Reasoning, 2022, 142(12):451-468.
[5] QIAO Junsheng, HU Baoqing. On(⊙, &)-fuzzy rough sets based on residuated and co-residuated lattices[J]. Fuzzy Sets and Systems, 2018, 336(7):54-86.
[6] 杨闻起. 环的次极大理想[J]. 纯粹数学与应用数学,2003,19(1):88-90. YANG Wenqi. Submaximal ideal of the ring[J]. Pure and Applied Mathematics, 2003, 19(1):88-90.
[7] 陈露. 半群的次极大理想与次极小理想[J]. 数学理论与应用,2005,25(3):107-110. CHEN Lu. Submaximal ideal and subminimal ideal of semigroup[J]. Mathematical Theory and Applications, 2005, 25(3):107-110.
[8] 欧启通. 半环的次极大理想[J]. 广西民族大学学报,2008,14(3):50-53. OU Qitong. Submaximal ideal of semiring[J]. Journal of Guangxi University for Nationalities, 2008, 14(3):50-53.
[9] 杨闻起. BCK-代数的次极大理想[J]. 西南师范大学学报,2004,29(1):38-40. YANG Wenqi. Submaximal ideal of the BCK-alagebra[J]. Journal of Southwest China Normal University, 2004, 29(1):38-40.
[10] 李小杰,吴洪博. BR0代数的次极大⊗滤子[J]. 云南师范大学学报,2008,28(4):10-12. LI Xiaojie, WU Hongbo. Submaximal ⊗ filter of the BR0 algebra[J]. Journal of Yunnan Normal University, 2008, 28(4):10-12.
[11] 姚卫. Heyting代数中滤子与同构定理及其范畴Heyt[D]. 西安:陕西师范大学,2005. YAO Wei. Filters and isomorphism theorems in Heyting algebra and its category Heyt[D]. Xian: Shaanxi Normal University, 2005.
[12] 刘德贤,卢涛,陈英. 条件并半格上的相对极大理想[J]. 吉林师范大学学报(自然科学版),2012,33(3):26-27. LIU Dexian, LU Tao, CHEN Ying. Relative maximal ideals in conditional join-semilattices[J]. Jilin Normal University Journal(Natual Science Edition), 2012, 33(3):26-27.
[13] 路玲霞,王群. 条件交半格中的相对极大滤子[J]. 模糊系统与数学,2011,25(2):66-70. LU Lingxia, WANG Qun. Relative maximal filters in conditional semilattices[J]. Fuzzy Systems and Mathematics, 2011, 25(2):66-70.
[14] 陈露,蒲义书. BCK-代数中子集的次极大理想[J]. 纯粹数学与应用数学,2007,23(3):361-365. CHEN Lu, PU Yishu. Subsets submaximum ideal of the BCK-algebra[J]. Pure and Applied Mathematics, 2007, 23(3):361-365.
[15] 路玲霞,姚卫. 分配格的滤子格是空间式frame的新证明[J]. 模糊系统与数学,2007,21(4):43-46. LU Lingxia, YAO Wei. A new proof for the filter-lattice of a distributive lattice to be a spatial frame[J]. Fuzzy Systems and Mathematics, 2007, 21(4):43-46.
[16] 路玲霞,毕建芝. 剩余格的滤子格成为空间式frame的若干充要条件[C] // 中国系统工程学会模糊数学与模糊系统专委会第十三届年会. 西安: 陕西师范大学出版社,2006:115-118. LU Lingxia, BI Jianzhi. Some equivalent conditions for the filter-lattice of a residuated lattice to be a spatial frame[C] // The 13th Annual Conference of Fuzzy Mathematics and Systems Association of the Systems Engineering Society of China, Xian: Shaanxi Normal University Publishing House Co., Ltd., 2006:115-118.
[17] 王国俊,郑慕聪,刘艳. 余剩余格的理想和嵌入定理[J]. 陕西师范大学学报(自然科学版),2006,34(4):1-6. WANG Guojun, ZHENG Mucong, LIU Yan. Ideals and embedding theorem of co-residuated lattices[J]. Journal of Shaanxi Normal University(Natural Science Edition), 2006, 34(4):1-6.
[18] 姚卫,路玲霞. 序与格论基础[M]. 北京: 清华大学出版社,2023. YAO Wei, LU Lingxia. Fundamentals of order and lattice theory[M]. Beijing: Tsinghua University Press, 2023.
[19] 郑崇友,樊磊,崔宏斌. Frame与连续格[M]. 北京:首都师范大学出版社,1994. ZHENG Chongyou, FAN Lei, CUI Hongbin. Frame and continuous lattice[M]. Beijing: Capital Normal University Press, 1994.
[1] QIN Xue-cheng, LIU Chun-hui*. The lattice of fuzzy ⊙-ideals in regular residuated lattices [J]. J4, 2011, 46(8): 73-76.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd