《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (2): 104-108.doi: 10.6040/j.issn.1671-9352.0.2019.068
• • 上一篇
曹发生,肖方
CAO Fa-sheng, XIAO Fang
摘要： 研究了布尔代数和模态代数的主同余,严格按照布尔代数和模态代数的主同余的定义,给出了布尔代数和模态代数的主同余刻画。
中图分类号:
| [1] BURRIS S, SANKAPPANAVAR H P. A course in universal algebra[M]. New York: Springer Verlag, 1981. [2] GRATZER George. Universal algebra[M]. New York: Springer Verlag, 1979. [3] BLYTH T, VARLET J. Principal congruences on some lattice-ordered algebras[J]. Discrete Mathematics, 1990, 81(3):323-329. [4] CELANI S A. Modal Tarski algebras[J]. Reports on Mathematical Logic, 2005, 39:113-126. [5] FANG Jie, SUN Zhongju. Principal congruences on S1-algebras[J]. Algebra Colloq, 2013, 20(3):427-434. [6] JANSANA R, SAN MARTÍN H J. On principal congruences in distributive lattices with a commutative monoidal operation and an implication[J]. Studia Logica, 2019, 107(2):351-374. [7] LAKSTER H. Principal congruences of pseudocomplemented distributive lattices[J]. Proceedings of the American Mathematical Society, 1973, 37(1):32-36. [8] PALMA C, SANTOS R. Principal congruences on semi-de Morgan algebras[J]. Studia Logica, 2001, 67(1):75-88. [9] SAN MARTÍN H J. Principal congruences in weak Heyting algebras[J]. Algebra Universalis, 2016, 75(4):405-418. [10] SAN MARTÍN H J. On congruences in weak implicative semi-lattices[J]. Soft Computing, 2017, 21(12):3167-3176. [11] SANKAPPANAVR H P. Principal congruences on psdudocomplemented on Morgan algebras[J]. Proc Amer Math Soc, 1987(33):3-11. [12] SANKAPPANAVR, H P, DE CARVALHO Júlia Vaz. Congruence properties of pseudocomplemented de Morgan algebras[J]. Mathematical Logic Quarterly, 2014, 60(6):425-436. [13] SANKAPPANAVR, H P. Principal congruences of double demi-p-lattices[J]. Algebra Universalis, 1990, 27(2):248-253. [14] LUO C W. A special kind of principal congruences on MS-algebras[J]. Acta Mathematica Scientia, 2008, 28(2):315-320. [15] 宋振明, 徐杨. 格蕴涵代数上的同余关系[J]. 应用数学, 1997, 10(3):121-124. SONG Zhenming, XU Yang. Congruence relations on lattice implication algebras[J]. Mathematica Applicata, 1997, 10(3):121-124. [16] 曹发生, 王驹, 蒋运承. 格L的元与主同余的关系[J]. 西南大学学报(自然科学版), 2009, 31(12):87-91. CAO Fasheng, WANG Ju, JIANG Yuncheng. The relationship of element of lattice L and principal congruence on it[J]. Journal of Southwest University(Natural Science Edition), 2009, 31(12):87-91. [17] 曹发生, 王驹, 蒋运承. 有单位元的环的主同余[J]. 江西师范大学学报(自然科学版), 2010, 34(2):192-194, 214. CAO Fasheng. Principal congruence on ring with identity[J]. Journal of Jiangxi Normal University(Natural Sciences Edition), 2010, 34(2):192-194, 214. [18] 曹发生. 布尔格的主同余[J].四川师范大学学报(自然科学版),2012,35(2):236-239. CAO Fasheng. Principal congruence on boolean lattices[J]. Journal of Sichuan Normal University(Natural Science Edition), 2012, 35(2):236-239. [19] 曹发生. Hamilton群的主同余[J].数学的实践与认识, 2013, 43(15):255-258. CAO Fasheng. Principal congruence on Hamilton groups[J]. Mathematics in Practice and Theory, 2013, 43(15):255-258. [20] 叶林, 曹发生. 格的标准元和分配元的主同余[J]. 山东大学学报(理学版), 2010, 45(11):63-66, 72. YE Lin, CAO Fasheng. Principal congruence on the standard and distributive elements of a lattice[J]. Journal of Shandong University, 2010, 45(11):63-66, 72. |
| [1] | 刘莉君. 布尔代数上triple-δ-导子的特征及性质[J]. 山东大学学报（理学版）, 2017, 52(11): 95-99. |
| [2] | 刘卫锋. 布尔代数的软商布尔代数[J]. 山东大学学报（理学版）, 2015, 50(08): 57-61. |
| [3] | 刘卫锋,杜迎雪,许宏伟. 区间软布尔代数[J]. 山东大学学报（理学版）, 2014, 49(2): 104-110. |
| [4] | 冯敏1,辛小龙1*,李毅君1,2. MV-代数上的f导子和g导子[J]. 山东大学学报（理学版）, 2014, 49(06): 50-56. |
| [5] | 刘卫锋. 软布尔代数[J]. J4, 2013, 48(8): 56-62. |
| [6] | 刘春辉1,2. 布尔代数的区间值(∈,∈∨ q)模糊子代数[J]. J4, 2013, 48(10): 94-98. |
| [7] | 叶林1,曹发生2. 格的标准元和分配元的主同余[J]. J4, 2010, 45(11): 63-66. |
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