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J4 ›› 2013, Vol. 48 ›› Issue (8): 36-40.

• 论文 • 上一篇    下一篇

集合Λ上的半格Γ确定的二元关系半群PΓ(Λ×Λ)的幂等元

林屏峰,曾伟,曾纯一   

  1. 西南民族大学 预科教育学院, 四川 成都 610041
  • 收稿日期:2012-09-24 出版日期:2013-08-20 发布日期:2013-08-21
  • 作者简介:林屏峰(1982- ),讲师,硕士,研究方向为半群代数. Email:p.f.lin@126.com
  • 基金资助:

    中央高校基本科研业务费专项项目(12NZYQN29、12NZYTD21)

Idempotents of semigroup PΓ(Λ×Λ) of binary relations determined by the semilattice Γ on the set Λ

LIN Ping-feng, ZENG Wei, ZENG Chun-yi   

  1. School of Preparatory Courses, Southwest University for Nationalities, Chengdu 610041, Sichuan, China
  • Received:2012-09-24 Online:2013-08-20 Published:2013-08-21

摘要:

 设Λ是任意的非空集合,Γ是集合Λ上的半格,半群PΓ(Λ×Λ)是由集合Λ上的半格Γ确定的二元关系半群。利用半格的性质,获得了半群PΓ(Λ×Λ)的幂等元性质,并且构造出了一类幂等元,并刻画了它的左单位元。

关键词: 二元关系半群;幂等元;左单位元

Abstract:

Let Λ be an arbitrary nonempty set, and Γ be a semilattice on the set Λ, semigroup PΓ(Λ×Λ) is a semigroup of binary relations determined by the semilattice Γ on the set Λ. Use of the nature of the semilattice,characteristics of idempotents of the semigroup PΓ(Λ×Λ) are obtained,and a class of idempotents is constructed; Finally, left units of the semigroup PΓ(Λ×Λ) are characterized.

Key words:  semigroup of binary relations; idempotents; left units

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