Residual finiteness and related properties in monounary algebras and their direct products
Residual finiteness and related properties in monounary algebras and their direct products
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一元代数及其直积中的剩余有限性和相关性质
DOI：
10.1007/s00012-021-00727-4
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
B. Witt
中科院分区：
文献类型：
--
作者：
B. Witt
在残差有限性、强/弱子代数可分性和完全可分性的基础上，讨论了一元代数的直积与其分量之间的关系。对于这些性质$\mathcal{P}$，我们给出一个图形判据$\mathcal{C_P}$，使得一元代数$ a $具有性质$\mathcal{P}$当且仅当它满足$\mathcal{C_P}$。我们还证明了对于一元代数的直积$ a \乘以B$, $ a \乘以B$具有性质$\mathcal{P}$，当且仅当下列条件之一成立：$ a $和$B$都具有性质$\mathcal{P}$，或者$ a $或$B$中至少有一个是后界的，这是一个支配直接积并保证所有$\mathcal{P}$成立的特殊性质。
In this paper we discuss the relationship between direct products of monounary algebras and their components, with respect to the properties of residual finiteness, strong/weak subalgebra separability, and complete separability. For each of these properties $\mathcal{P}$, we give a graphical criterion $\mathcal{C_P}$ such that a monounary algebra $A$ has property $\mathcal{P}$ if and only if it satisfies $\mathcal{C_P}$. We also show that for a direct product $A\times B$ of monounary algebras, $A\times B$ has property $\mathcal{P}$ if and only if one of the following is true: either both $A$ and $B$ have property $\mathcal{P}$, or at least one of $A$ or $B$ are backwards-bounded, a special property which dominates direct products and which guarantees all $\mathcal{P}$ hold.
影响因子：
0.7
作者：
MILLER C
通讯作者：
MILLER C