集合Λ上的半格Γ确定的二元关系半群PΓ(Λ×Λ)的不可分解元

doi:10.6040/j.issn.1671-9352.0.2015.060

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 12-15.doi: 10.6040/j.issn.1671-9352.0.2015.060

集合Λ上的半格Γ确定的二元关系半群P_Γ(Λ×Λ)的不可分解元

林屏峰

西南民族大学预科教育学院, 四川成都 610041

收稿日期:2015-02-02 出版日期:2016-02-16 发布日期:2016-03-11
作者简介:林屏峰(1982— ),男,硕士,讲师,研究方向为半群代数. E-mail:p.f.lin@126.com
基金资助:
中央高校基本科研业务费专项项目(2015NZYQN38)

Non-solvabla elements of semigroup P_Γ(Λ×Λ)of binary relations determined by the semilattice Γ on the set Λ

LIN Ping-feng

School of Preparatory Courses, Southwest University for Nationalities, Chengdu 610041, Sichuan, China

Received:2015-02-02 Online:2016-02-16 Published:2016-03-11

摘要/Abstract

摘要： 设Λ是任意的非空集合,Γ是集合Λ上的半格,P_Γ(Λ×Λ)是集合Λ上的半格Γ确定的二元关系半群。得到了半群P_Γ(Λ×Λ)的不可分解元的一个充分必要条件,并且在一定条件下找到了一类不可分解元。

关键词: 不可分解元, 二元关系半群, 半格

Abstract: Let Λ be an arbitrary nonempty set, and Γ be a semilattice on the set Λ. Let P_Γ(Λ×Λ)is a semigroup of binary relations determined by the semilattice Γ on the set Λ. In the semigroup P_Γ(Λ×Λ), a necessary and sufficient condition of non-solvable elements is obtained,and a class of non-solvable elements is found under certain conditions.

Key words: semigroup of binary relations, non-solvable elements, semilattices

中图分类号:

O152.7

林屏峰. 集合Λ上的半格Γ确定的二元关系半群P_Γ(Λ×Λ)的不可分解元[J]. 山东大学学报（理学版）, 2016, 51(2): 12-15.

LIN Ping-feng. Non-solvabla elements of semigroup P_Γ(Λ×Λ)of binary relations determined by the semilattice Γ on the set Λ[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 12-15.

参考文献

[1] PLEMMONS R J, WEST M T. On the semigroup of binary relations[J]. Pacific J Math, 1970, 35:743-753.
[2] PLEMMONS R J, SCHEIN B M. Groups of binary relations[J]. Semigroup Forum, 1970, 1(1):267-271.
[3] SCHWARZ S. On idempotent binary relations on a finite set[J]. Czech J Math, 1970, 20:696-702.
[4] KONIECZNY J. The semigroup generated by regular Boolean matrices[J]. South Asian Bull of Math, 2002, 25:627-641.
[5] CHASE K. New semigroups of binary relations[J]. Semigroup Forum, 1979, 18(1):79-82.
[6] CHASE K. Sandwish semigroups of binary relations[J]. Discrete Math, 1979, 28:231-236.
[7] 林屏峰. 集合I到集合Λ上的二元关系半群P_θ(I×Λ)的生成集和Green-关系[J].西南民族大学学报(自然科学版), 2010,36(1):44-49. LIN Pingfeng. Generating sets and Greens relations for semigroup P_θ(I×Λ)of all binary relations form a set I to a set Λ[J]. Journal of Southwest University for Nationlities(Natural Science), 2010, 36(1):44-49.
[8] 林屏峰. 集合Λ上的半格Γ确定的二元关系半群P_Γ(Λ×Λ)的基本性质[J].西南民族大学学报(自然科学版), 2012,38(4):529-532. LIN Pingfeng. Some properties of semigroup P_Γ(Λ×Λ) binary relations determined by the semilattice Γ on the set Λ[J]. Journal of Southwest University for Nationlities(Natural Science), 2012, 38(4):529-532.
[9] 林屏峰,曾伟,曾纯一. 集合Λ上的半格Γ确定的二元关系半群P_Γ(Λ×Λ)的幂等元[J].山东大学学报(理学版), 2013,48(8):36-40. LIN Pingfeng, ZENG Wei, ZENG Chunyi. Idempotents of semigroup P_Γ(Λ×Λ)of binary relations determined by the semilattice Γ on the set Λ[J]. Journal of Shandong University(Natural Science), 2013, 48(8):36-40.
[10] BIRKHOFF G. Lattice theory[M]. New York: American Mathematical Society, 1967.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

集合Λ上的半格Γ确定的二元关系半群P_Γ(Λ×Λ)的不可分解元

Non-solvabla elements of semigroup P_Γ(Λ×Λ)of binary relations determined by the semilattice Γ on the set Λ

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 8

多维度评价

本文评价

推荐阅读 0

[1]	邵勇. 半格序完全正则周期半群[J]. 山东大学学报（理学版）, 2018, 53(10): 1-5.
[2]	林屏峰,曾伟,曾纯一. 集合Λ上的半格Γ确定的二元关系半群PΓ(Λ×Λ)的幂等元[J]. J4, 2013, 48(8): 36-40.
[3]	苏玉,孔祥智*. L^ρC-正则半群[J]. J4, 2011, 46(4): 68-69.
[4]	刘开振孔祥智. 半超富足半群的结构[J]. J4, 2010, 45(1): 86-88.
[5]	毕晓冬. 左拟正规带的张量积[J]. J4, 2009, 44(8): 39-41.
[6]	毕晓冬 . 左拟正规带的自由积[J]. J4, 2008, 43(6): 83-86 .
[7]	丁月,孔祥智 . H#-富足半群[J]. J4, 2008, 43(4): 55-57 .
[8]	毕晓冬 . 完全正则半群的一个构造方法[J]. J4, 2007, 42(1): 40-43 .

集合Λ上的半格Γ确定的二元关系半群PΓ(Λ×Λ)的不可分解元

Non-solvabla elements of semigroup PΓ(Λ×Λ)of binary relations determined by the semilattice Γ on the set Λ

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 8

多维度评价

本文评价

推荐阅读 0

集合Λ上的半格Γ确定的二元关系半群P_Γ(Λ×Λ)的不可分解元

Non-solvabla elements of semigroup P_Γ(Λ×Λ)of binary relations determined by the semilattice Γ on the set Λ