论文标题
统一的伯克霍夫
Uniform Birkhoff
论文作者
论文摘要
我们表明，有限生成的代数，即有限生成的代数$ c $在有限的产品，同型图像和亚代词中关闭的代数$ c $可以通过$ c $的$ c $上的$ c $上的$ c $上的$ c $上的$ c $上的$ C $上的$ C $上的$ C $上的$ C $上的$ c $ a $ c $ a $ c $的$ c $ a $ c $ a $ c $ a $ c $的$ c $ a $ c $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ c $ a $ c $ a $ c $ the $ c $的$ c $ a $ a $ a $ a $ c。 $ a $的术语克隆在均匀性$ u $和$ a $的术语术语中的均匀性均匀性方面定义明确且均匀连续。我们的结果统一了描述有限代数的伪伏和单个寡形代代数产生的假性化的假性定理。
We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free algebra for $C$: the members of $C$ then are precisely those finitely generated algebras $A$ for which the natural mapping from the free algebra onto the term clone of $A$ is well-defined and uniformly continuous with respect to the uniformity $U$ and the uniformity of pointwise convergence on the term clone of $A$, respectively. Our result unifies earlier theorems describing pseudovarieties of finite algebras and the pseudovariety generated by a single oligomorphic algebra.
