弱左型B半群的半格分解

The semilattice decomposition of weakly left type B semigroups

弱型B半群是半富足半群范围的一类广义逆半群,而幂等元法是研究此类半群的重要方法。作为推广,本文首先通过幂等元法介绍了弱型B一元半群的定义,并给出了此类一元半群的基本性质,特别地,利用上述一元半群的基本性质,得到了任意一元半群为弱左型B半群的等价条件。最后,文章给出了弱左型B半群的半格分解,得到了一些结果。

Weakly type Bsemigroups are generalized inverse semigroups on semi-abundant semigroups.This paperstudied the semigroupby the method of idempotent.As a generalization, the notion of a weakly type B unary semigroupwas introduced by an idempotent method.Some basic properties of such unary semigroupwere given.Moreover, some equivalent conditions for an arbitrary unary semigroup to be a weakly left type Bsemigroupwereobtained.Finally, asemilattice decomposition of a weakly left Bsemigroupwas given, and some resultswere obtained.