### Principal congruence on Tarski algebra and modal algebra

CAO Fa-sheng

1. Department of Cognitive Science, Guizhou Minzu University, Guiyang 550025, Guizhou, China
• Online:2020-10-20 Published:2020-10-07

Abstract: The principal congruences of Tarski algebras and modal algebras are studied. Combined with the result of principal congruence of Boolean algebra, the characterization of principal congruence of Tarski algebra and modal algebra is given.

CLC Number:

• O153.5
 [1] BLYTH T, VARLET J. Principal congruences on some lattice-ordered algebras[J]. Discrete Mathematics, 1990, 81(3):323-329.[2] BURRIS S, SANKAPPANAVAR H P. A course in universal algebra[M]. New York: Springer-Verlag, 1981.[3] CELANI S A. Modal Tarski algebras[J]. Reports on Mathematical Logic, 2005, 39(39):113-126.[4] FANG Jie, SUN Zhongju. Principal congruences on S1-algebras[J]. Algebra Colloq, 2013, 20(3):427-434.[5] GRÄTZER G. Universal algebra[M]. New York: Springer-Verlag, 1979.[6] JANSANA R, MARTÍN H J S. On principal congruences in distributive lattices with a commutative monoidal operation and an implication[J]. Studia Logica, 2018(3):1-24.[7] LAKSER H. Principal congruences of pseudocomplemented distributive lattices[J]. Proceedings of the American Mathematical Society, 1973, 37(1):32-36.[8] LUO C. A special kind of principal congruences on MS-algebras[J]. Acta Mathematica Scientia, 2008, 28(2):315-320.[9] SAN MARTÍN Hernán Javier. Principal congruences in weak Heyting algebras[J]. Algebra Universalis, 2016, 75:405-418.[10] SAN MARTÍN Hernán Javier. On congruences in weak implicative semi-lattices[J]. Soft Computing, 2016, 21(12):1-10.[11] PALMA C, SANTOS R. Principal congruences on semi-de morgan algebras[J]. Studia Logica, 2001, 67(1):75-88.[12] SANKAPPANAVAR H P. Principal congruences on psdudo-complemented on Morgan algebras[J]. Proc Amer Math Soc, 1987(33):3-11.[13] SANKAPPANAVAR H P, VAZ DE CARVALHO J. Congruence properties of pseudocomplemented de Morgan algebras[J]. Mathematical Logic Quarterly, 2014, 60(6):425-436.[14] SANKAPPANAVA H P. Principal congruences of double demi-p-lattices[J]. Algebra Universalis, 1990, 27(2):248-253.[15] 曹发生,王驹,蒋运承.格L的元与它的主同余的关系[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 Southwest University(Nature Science Edition), 2009, 31(12):87-91.[16] 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. CAO Fasheng, WANG Ju, JIANG Yuncheng. Principal Congruence on ring with identity[J]. Journal of Jiangxi Normal University(Nature Science Edition), 2010, 34(2):192-194.[17] 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(Nature Science Edition), 2012, 35(2):236-239.[18] 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.[19] 曹发生,肖方. 模态代数的主同余[J].山东大学学报(理学版), 2020,55(2):104-108. CAO Fasheng, XIAO Fang. Principal congruences on modal algebras[J]. Journal of Shandong University(Nature Science), 2020, 55(2):104-108.[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):63-67. YE Lin, CAO Fasheng. Principal congruence on the standard and distributive elements of lattice[J]. Journal of Shandong University(Nature Science), 2010, 45(11):63-67.
 [1] CAO Fa-sheng, XIAO Fang. Principal congruences on modal algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 104-108. [2] YE Lin1, CAO Fa-sheng2. Principal congruence on the standard and distributive elements of a lattice [J]. J4, 2010, 45(11): 63-66.
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