论文标题
乘法表和单词hyperbolicity在半群，单体和组的免费产品中
Multiplication tables and word-hyperbolicity in free products of semigroups, monoids, and groups
论文作者
论文摘要
本文研究了单词hyperbolic semogroups和himoids的特性，即具有与邓肯和吉尔曼（Duncan＆Gilman）定义的常规梳子相对于常规梳理表的无上下文乘法表的特性。特别是，考虑使用免费产品下的单词hyperbolicity。在所涉及的半群中的轻度条件下，满足，例如通过单型或常规的半群，我们证明了两个单词hyperbolic semigroups的半原始产物再次是单词hyperbolic。类似地，对身份元素的代表性唯一性具有轻微的条件，例如通过小组，我们证明了两个单词hyperbolic单词的无单型产物是单词hyperbolic。这些方法在理论上是语言是一般的，并且同样适用于具有$ \ Mathbf {C} $ - 乘法表的半群，单型或组，其中$ \ Mathbf {c} $是任何反向封闭的super-$ $ $ \ $ \ operatateName {afl} $，就Greibach而言。特别是，我们推断出两组具有$ \ operatorname {et0l} $ resp的免费产品。索引乘法表再次具有$ \ operatatorName {et0l} $ resp。索引乘法表。
This article studies the properties of word-hyperbolic semigroups and monoids, i.e. those having context-free multiplication tables with respect to a regular combing, as defined by Duncan & Gilman. In particular, the preservation of word-hyperbolicity under taking free products is considered. Under mild conditions on the semigroups involved, satisfied e.g. by monoids or regular semigroups, we prove that the semigroup free product of two word-hyperbolic semigroups is again word-hyperbolic. Analogously, with a mild condition on the uniqueness of representation for the identity element, satisfied e.g. by groups, we prove that the monoid free product of two word-hyperbolic monoids is word-hyperbolic. The methods are language-theoretically general, and apply equally well to semigroups, monoids, or groups with a $\mathbf{C}$-multiplication table, where $\mathbf{C}$ is any reversal-closed super-$\operatorname{AFL}$, in the sense of Greibach. In particular, we deduce that the free product of two groups with $\operatorname{ET0L}$ resp. indexed multiplication tables again has an $\operatorname{ET0L}$ resp. indexed multiplication table.
