自由Clifford幺半群和含恒等元的自由半格的图表示

详细信息

Graph Representations of a Free Clifford Monoid and a Free Semilattice with Identity

摘要: 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.
- 自由Clifford幺半群 /
- 含恒等元的自由半格 /
- 字树
Abstract: 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.
- free Clifford monoid /
- free semilattice with identity /
- word tree