论文标题
通用克隆代数
Universal Clone Algebra
论文作者
论文摘要
我们为代数和克隆开发了一个新的通用框架，称为通用克隆代数。限制操作的代数和克隆是通用代数的t-Elgebras和clone代数是通用克隆代数。最近引入了克隆代数，发现了一个单排，纯粹的代数克隆理论，而本文首先引入了T-代数。我们提出了一种将代数和克隆编纂为T-代数和克隆代数的方法。我们提供了具体的例子，表明在代数和克隆方面翻译通用克隆代数中的一般结果，在通用代数中提供了更强大的已知定理版本。我们将此方法应用于Birkhoff的HSP定理以及Birkhoff定理的最新拓扑版本。
We develop a new general framework for algebras and clones, called Universal Clone Algebra. Algebras and clones of finitary operations are to Universal Algebra what t-algebras and clone algebras are to Universal Clone Algebra. Clone algebras have been recently introduced to found a one-sorted, purely algebraic theory of clones, while t-algebras are first introduced in this article. We present a method to codify algebras and clones into t-algebras and clone algebras, respectively. We provide concrete examples showing that general results in Universal Clone Algebra, when translated in terms of algebras and clones, give more powerful versions of known theorems in Universal Algebra. We apply this methodology to Birkhoff's HSP theorem and to the recent topological versions of Birkhoff's theorem.
