具有唯一左单位的二元关系半群Pγ(λ×λ)

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

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．

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.