论文标题
单一代数及其直接产品的剩余有限性和相关特性
Residual Finiteness and Related Properties in Monounary Algebras and their Direct Products
论文作者
论文摘要
在本文中，我们讨论了单位代数的直接产物及其组件之间的关系，就剩余有限性，强/弱的亚代词可分离性和完全可分离性的特性而言。对于这些属性$ \ MATHCAL {P} $，我们给出一个图形标准$ \ MATHCAL {c_p} $，以便在且仅当满足$ \ nathcal {c_p} $时，只有当它满足$ \ mathcal {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。
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.
