JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (4): 1-8.doi: 10.6040/j.issn.1671-9352.0.2022.590

   

Special elements, ideals in involutive m-semilattices and its categorical properties

LIANG Shaohui, ZHANG Xueting, XIA Xiaogang   

  1. School of Science, Xian University of Science and Technology, Xian 710100, Shaanxi, China
  • Published:2024-04-12

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Abstract: The concept of involutive m-semilattices is given, and a series of important properties of involutive m-semilattices are obtained. The two order relationships ≪ and  are defined in involutive m-semilattices, and the interrelationships between the involutive m-semilattices *, special element and ≪、  are discussed. The subinvolutive m-semilattices are constructed by using special elements. The structures of ideals and filters in involutive m-semilattices are studied, the concrete forms of generating ideals and filters from elements are obtained. The definition of the category of involutive m-semilattices is introduced, and the specific form of the product of the category of involutive m-semilattices is discussed, and the limit structure of the category of involutive m-semilattices is obtained. It is proved that the category of involutive m-semilattices is complete.

Key words: involutive m-semilattice, ideal, filter, category, limit

CLC Number: 

  • O153.1
[1] MULVEY C J. & [J]. Rendiconti del Circolo Matematico di Palermo, 1986, 12(2):99-104.
[2] MULVEY C J, PELLETIER J W. On the quantisation of point[J]. Journal of Pure and Applied Algebra, 2001, 159(2):231-295.
[3] NAWAZ M. Quantales: quantale sets[D]. Sussex, UK: University of Sussex, 1985.
[4] NIEFIED S B, ROSENTHAL K I. Strong De Morgans law and the spectrum of a commutative ring[J]. Journal of Algebra, 1985, 93(1):169-181.
[5] GIRARD J Y. Linera logic[J]. Theoreticd Computer Science, 1987, 50(1):1-102.
[6] ROSENTHOL K I. Quantales and their applications[M]. New York: Longman Scientific and Technical, 1990.
[7] ZHAO Dongsheng, ZHAO Bin. The categories of m-semilattices[J]. Northeastern Mathematical Journal, 1998, 14(4):419-430.
[8] 苏子祺,赵彬. m-半格中的滤子及其相关拓扑性质[J]. 吉林大学学报(理学版), 2022, 60(3):568-576. SU Ziqi, ZHAO Bin. Filtres in m-semilattices and their related topological properties[J]. Journal of Jilin University(Science Edition), 2022, 60(3):568-576.
[9] 周欣,赵彬. m-半格的粗糙模糊理想[J]. 吉林大学学报(理学版), 2015, 53(3):429-438. ZHOU Xin,ZHAO Bin. Rough fuzzy ideals of m-semilattices[J]. Journal of Jilin University(Science Edition), 2015, 53(3):429-438.
[10] 周欣. m-半格上的模糊理想与粗糙集[D]. 西安:陕西师范大学, 2015. ZHOU Xin. Fuzzy ideals and rough sets on m-semilattices[D]. Xian: Shaanxi Normal University, 2015.
[11] ZHOU Xin, ZHAO Bin, HAN Shengwei. Roughness in m-semilattices[J]. Journal of Intelligent & Fuzzy Systems, 2016, 30(4):2331-2338.
[12] 赵娜. m-半格矩阵的M-P广义逆[J]. 太原师范学院学报(自然科学版), 2018, 17(3):25-28. ZHAO Na. Generalized M-P inverse of m-semilattice matrix[J]. Journal of Taiyuan Normal University(Natural Science-Edition), 2018, 17(3):25-28.
[13] 周异辉,马君亮. 对合Quantale中对合运算与特殊元的关系[J]. 模糊系统与数学, 2008, 22(1):62-66. ZHOU Yihui, MA Junliang. The relation of involution and special elements in involutive quantales[J]. Fuzzy Systems and Mathematics, 2008, 22(1):62-66.
[14] 王顺钦. Quantic格与Quantale中若干问题的研究[D]. 西安:陕西师范大学, 2007. WANG Shunqin. Research on some questions in quantic lattices and quantales[D]. Xian: Shaanxi Normal University, 2007.
[15] 赵彬. 拓扑分子格范畴中的极限结构[J]. 科学通报, 1996, 41(8):680-682. ZHAO Bin. The limit structure in the category of topological molecular lattices[J]. Chinese Science Bulletin, 1996, 41(8):680-682.
[16] 刘智斌. Quantale中若干问题的研究[D]. 西安:陕西师范大学, 2004. LIU Zhibin. Some researches on quantale[D]. Xian: Shaanxi Normal University, 2004.
[17] 赵彬,梁少辉. 双Quantale模范畴[J]. 数学学报, 2009, 52(4):821-832. ZHAO Bin, LIANG Shaohui. The category of double quantale modules[J]. Acta Mathematica Sinica, 2009, 52(4):821-832.
[18] 肖滢. 对合Quantale及其范畴性质[D]. 西安:陕西师范大学, 2005. XIAO Ying. Involutive quantale and its categorical properties[D]. Xian: Shaanxi Normal University, 2005.
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