右型A半群的F-覆盖

F-Covers for Right Type-A Semigroups

中文关键词:  右型$A$半群  $F$-rpp半群  左消去幺半群  $\mathcal{L}^*$-同态  $^*$-同态  $F$-覆盖.

英文关键词:right type-$A$ semigroup  $F$-rpp semigroup  left cancellative monoid  $\mathcal{L}^*$-homomorphism  $*$-homomorphism  $F$-cover.

中文摘要:

      右适当半群$S$称为型$F$的,如果$S$是$F$-rpp半群.一个型$F$的右适当半群$T$称为另一个右型$A$半群$S$的$F$-覆盖,如果$S$是$T$的$\mathcal{L}^*$-同态像.本文的目的是要证明任何的右型$A$半群都有$F$-覆盖,并给出$F$-覆盖的结构.此结果推广了逆半群的相关结果.

英文摘要:

      A right adequate semigroup of type $F$ is defined as a right adequate semigroup which is an $F$-rpp semigroup. A right adequate semigroup $T$ of type $F$ is called an $F$-cover for a right type-$A$ semigroup $S$ if $S$ is the image of $T$ under an ${\cal L}^*$-homomorphism. In this paper, we will prove that any right type-$A$ monoid has $F$-covers and then establish the structure of $F$-covers for a given right type-$A$ monoid. Our results extend and enrich the related results for inverse semigroups.