论文标题
椭圆度均匀的复合体系列的路径半群
Semigroup of paths on a family of complexes with uniform ellipticity
论文作者
论文摘要
这是专门用于构建有限呈现的无限尼尔 - 序列的论文周期的第三部分，满足了身份$ x^9 = 0 $。该构造解决了L. N. Shevrin和M. V. Sapir的问题，例如在Sverdlovsk笔记本中提出的问题。半群被实现为一组特殊椭圆形复合物系列的路径编码。在循环的第一篇论文中有限定义的零半群：具有均匀椭圆的复合物，用一组几何特性构建了一系列复合物。在该系列的第二次确定性色彩的第二件作品中，在构造的复合物的顶点和边缘引入了有限字母编码。证明了这种着色的确定性属性，这使得在复合物上的一系列路径上引入了有限的定义关系集。在本文中，我们描述了一种将任意半群词简化为规范形式的算法。还证明，使用定义关系可以将包含带有周期9子词的单词降低至零。与足够长路径相对应的单词编码不会降低到零，也不会改变其长度，也就是说，引入的半群是无限的。
This is the third part of a cycle of papers devoted to the construction of a finitely presented infinite nil-semigroup satisfying the identity $x^9 = 0$. This construction answers the problem of L. N. Shevrin and M. V. Sapir, posed, for example, in the Sverdlovsk notebook. A semigroup is realized as a set of path encodings on a family of special uniformly elliptic complexes. In the first paper of the cycle Finitely defined nil semigroup: complexes with uniform ellipticity, a sequence of complexes was constructed with a set of geometric properties. In the second work of the series Deterministic Coloring of a Family of Complexes a finite letter encoding was introduced on the vertices and edges of the constructed complexes. The deterministic property of such a coloring was proved, which makes it possible to introduce a finite set of defining relations on the set of words-codings of paths on complexes. In this paper, we describe an algorithm for reducing an arbitrary semigroup word to canonical form. It is also proved that a word containing a subword with period 9 can be reduced to zero using defining relations. Word encodings corresponding to sufficiently long paths are not reduced to zero and do not change their length, that is, the introduced semigroup is infinite.
