自由Clifford幺半群和含恒等元的自由半格的图表示

证明了非空集合$X$上自由Clifford幺半群$C_{X}$与双根字树集合$B_{X}$的某个子集并上一个恒等元所得的半群$\overline{B_{X}}$同构, 并且考察了$B_{X}$与$\overline{B_{X}}$的关系. 另外, 还证明了含恒等元的自由半格$Y_{X}$与有根字树集合$T_{X}$的某个子集并上一个恒等元所得的半群$\overline{T_{X}}$同构.

GRAPH REPRESENTATIONS OF A FREE CLIFFORD MONOID AND A FREE SEMILATTICE WITH IDENTITY

The following conclusion is shown that a free Clifford monoid $C_{X}$ on X is isomorphic to a monoid $\overline{B_{X}}$ obtained by a subset of $B_{X}$, which is the set of all birooted word trees on the same X, together with a new multiplication. Furthermore, the relation between $B_{X}$ and $\overline{B_{X}}$ is considered. Also, it is shown that there is an isomorphism from a free semilattice with identity $Y_{X}$ on X onto a monoid $\overline{T_{X}}$ obtained by a subset of $T_{X}$, which is the set of rooted word trees on the same X.