Some remarks on representations of fundamental generalized inverse $\ast$-semigroups(Semigroups, Formal Languages and Combinatorics on Words)
輝男 今岡, Isamu Inata, Hiroaki Yokoyama · Institutional Repositories DataBase (IRDB) · 1995
\mathrm{W}.\mathrm{D}$ .Munn [4] described that every fundamental inverse semigroup can be faith- fuly represented by isomorphisms among principal ideals of the semilattice of idem- potents of it.Also T.Imaoka [3] has given a generalization of the Preston-Vagner representation for generalized inverse $*$ -semigroups by using a concept of a struc- ture sandwich set of an inverse subsemigroup of the symmetric inverse semigroup on a set.In this paper, we shall construct a fundamental $\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{r}*$ -semigroup $\mathcal{F}\mathcal{G}\mathcal{I}_{X}(\pi)$ on a set $X$ with a partion $\pi$ : $X=\Sigma\{X.: i\in I\}$ , and obtain a faithful representation of a fundamental generalized $\mathrm{i}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{e}*$ -semigroup into $*$ -semigroup $F\mathcal{G}\mathcal{I}_{X()}\pi$ on a set $X(\pi)$ .