[1]齐彩霞,阳 城,郭兰坤*,等.S-格上的同余关系[J].四川师范大学学报(自然科学版),2019,(01):25.[doi:10.3969/j.issn.1001-8395.2019.01.003]
 QI Caixia,YANG Cheng,GUO Lankun,et al.The Congruence Relations on S-lattices[J].Journal of SichuanNormal University,2019,(01):25.[doi:10.3969/j.issn.1001-8395.2019.01.003]
点击复制

S-格上的同余关系()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年01期
页码:
25
栏目:
基础理论
出版日期:
2018-12-15

文章信息/Info

Title:
The Congruence Relations on S-lattices
文章编号:
1001-8395(2019)01-0025-05
作者:
齐彩霞1 阳 城1 郭兰坤1* 刘 丽2
1.湖南师范大学 数学与统计学院, 湖南 长沙 410006; 2.湖南大学 数学与计量经济学院, 湖南 长沙 410012
Author(s):
QI Caixia1 YANG Cheng1 GUO Lankun1 LIU Li2
1.College of Mathematics and Statistics, Hunan Normal University, Changsha 410006, Hunan; 2.College of Mathematics and Econometrics, Hunan University, Changsha 410012, Hunan
关键词:
S-格 同余 伪同余 同态 S-分配格
Keywords:
S-lattice congruence pseudo-congruence homomorphism S-distributive lattice
分类号:
153.1
DOI:
10.3969/j.issn.1001-8395.2019.01.003
文献标志码:
A
摘要:
引入S-格上的同余和伪同余,并研究两者的内在联系; 给出S-格上的同态定理,推广了经典格上同余的相关结论; 讨论分配S-格上同余关系,并证明分配S-格上的任意二元关系H可自然诱导1个包含H的最小S-格同余.
Abstract:
In this paper, the congruence and pseudo-congruence on S-lattices are introduced, and the connection between these two concepts is investigated. The homomorphism theory on S-lattices is established, which generalizes the corresponding results about the congruence on S-lattices. The congruence on S-distributive lattices is discussed, which shows that for any binary relation H on an S-lattice, a smallest congruence containing H can be naturally induced.

参考文献/References:

[1] DAVEY B A, PRIESTLEY H A. Introduction to Lattices and Order[M]. Cambridge:Cambridge University Press,2002.
[2] GIERZ G, HOFMANN K H, KEIMEL K, et al. Scott. Continuous Lattices and Domains[M]. Cambridge:Cambridge University Press,2003.
[3] WILLE R. Tensorial decomposition of concept lattice[J]. Order,1985,2:81-95.
[4] WILLE R. Subdirect decomposition of concept lattice[J]. Algebra Universalis,1983,17:275-287.
[5] ZHANG G Q, SHEN G Q. Approximable concepts, chu spaces, and information systems[J]. Theory and Applications of Categories,2006,17(5):80-102.
[6] HARTUNG G. A topological representation of lattices[J]. Algebra Universalis,1992,29:273-299.
[7] MADLENER K, REINERT B. Relating rewriting techniques on monoids and rings:congruences on monoids and ideals in monoid rings[J]. Theoretical Computer Science,1998,208:3-31.
[8] GTÄTZER G. Congruences in slim, planar, semimodular lattices:the swing lemma[J]. Acta Mathematica Scientia(Szeged),2015,81:381-397.
[9] GRÄTZER G. Congruences and prime-perspectivities in finite lattices[J]. Algebra Universalis,2015,74:351-359.
[10] REUTER K, WILLE R. Complete congruence relations of concept lattice[J]. Acta Mathematica Scientia,1987,51:319-327.
[11] KHOSRAVI R, LIANG X. On(po-)torsion free and principally weakly(po-)flat S-posets[J]. Categories and General Algebraic Structures with Applications,2018,8(1):35-49.
[12] LIANG X L, LUO Y F. On condition (PWP)w for S-poset[J]. Turkish J Mathematics,2015,39(6):796-809.
[13] FAKHRUDDIN S M. On the category of S-posets[J]. Acta Mathematica Scientia,1988,52:85-92.
[14] BULMAN-FLEMING S, LAAN V. Lazard's theorem for S-posets[J]. Mathematische Nachrichten,2005,278:1743-1755.
[15] BULMAN-FLEMING S, MAHMONDE M. The category of S-posets[J]. Semigroup Forum,2005,71:443-461.
[16] HOLLINGS C. Mathematics Across the Iron Curtain:a History of the Algebraic Theory of Semigroups[M]. Washington:American Mathematical Society,2014.

相似文献/References:

[1]钟纯真.关于群的同余格的一个注记[J].四川师范大学学报(自然科学版),1999,(04):52.
 ZHONG Chun zhen (Department of Mathematics,Neijiang Teachers College,Neijiang 00,et al.[J].Journal of SichuanNormal University,1999,(01):52.
[2]庞江宁.关于完全数与费马数的一个性质[J].四川师范大学学报(自然科学版),1989,(02):0.
 Pang Jiangning (Department of Mathematics).[J].Journal of SichuanNormal University,1989,(01):0.
[3]余全华,刘人丽.关于多项式 x~((p-1)p~s)+x~((p-2)p~s)+…+x~(2p~s)+x~(p~s)+1的不可约性判定问题[J].四川师范大学学报(自然科学版),1986,(02):0.
[4]魏晓伟,岳跃利*,黄春娥.L-集上的模糊泛代数[J].四川师范大学学报(自然科学版),2019,(01):63.[doi:10.3969/j.issn.1001-8395.2019.01.009]
 WEI Xiaowei,YUE Yueli,HUANG Chune.Fuzzy Universal Algebra on L-sets[J].Journal of SichuanNormal University,2019,(01):63.[doi:10.3969/j.issn.1001-8395.2019.01.009]

备注/Memo

备注/Memo:
收稿日期: 2018-06-29 接受日期:2018-07-12
基金项目:国家自然科学基金(11401195)、湖南省教育厅优秀青年项目(16B153)和湖湘青年英才支持计划
*通信作者简介:郭兰坤(1983—),男,副教授,主要从事格上拓扑学的研究,E-mail:lankun.guo@gmail.com
更新日期/Last Update: 2018-12-15