具有唯一左单位的二元关系半群Pγ(λ×λ)

基金项目:

中央高校基本科研业务费专项项目

详细信息

Semigroup Pγ(Λ×Λ) with the Unique Left Unit

School of Preparatory Courses,Southwest University for Nationalities,Chengdu 610041,Chain

Funds:

Central University of basic scientific research business special projects

摘要: 设 $\Lambda$ 是任意的非空集合， $\Gamma$ 是集合 $\Lambda$ 上的半格， ${\cal P}_{\Gamma}(\Lambda\times\Lambda)$ 是集合 $\Lambda$ 上的半格 $\Gamma$ 确定的二元关系半群．利用半群 ${\cal P}_{\Gamma}(\Lambda\times\Lambda)$ 的左单位已有的结论，获得了半群 ${\cal P}_{\Gamma}(\Lambda\times\Lambda)$ 的最大左单位，通过半群 ${\cal P}_{\Gamma}(\Lambda\times\Lambda)$ 的左单位的构造方法，研究半群 ${\cal P}_{\Gamma}(\Lambda\times\Lambda)$ 具有唯一左单位应该满足的条件．
- 二元关系半群 /
- 左单位 /
- 最大左单位 /
- 唯一左单位 /
- 列不可约二元关系
Abstract: Let $\Lambda$ be an arbitrary nonempty set, and $\Gamma$ be a semilattice on the set $\Lambda$ , ${\cal P}_{\Gamma}(\Lambda\times\Lambda)$ is a semigroup of binary relations determined by the semilattice $\Gamma$ on the set $\Lambda$ . In the semigroup ${\cal P}_{\Gamma}(\Lambda\times\Lambda)$ , by using the existing conclusions of left units, the greatest left unit is obtained. By employing constructive method of the left units, we find the conditions that this left unit must satisfy for the given senmigroup ${\cal P}_{\Gamma}(\Lambda\times\Lambda)$ to have a unique right unit.
- semigroup of binary relations /
- left units /
- the greatest left unit /
- the unique left unit /
- column-reducible binary relations