自由Clifford幺半群和含恒等元的自由半格的图表示

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\overlineB_X同构, 并且考察了B_X与\overlineB_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\overlineT_X同构.

Abstract: The following conclusion is shown that a free Clifford monoid C_X on X is isomorphic to a monoid \overlineB_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 \overlineB_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 \overlineT_X obtained by a subset of T_X, which is the set of rooted word trees on the same X.