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 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.

在本文中，我们讨论了一元代数的直接乘积与其成分之间的关​​系，包括剩余有限性，强/弱子代数可分离性和完全可分离性。对于这些属性\（{\ mathcal {P}} \），我们给出一个标准\（\ mathcal {C_P} \），使得一元代数\（A \）具有属性\（{\ mathcal {P} } \）当且仅当它满足\（\ mathcal {C_P} \）。我们还表明，对于一元代数的直接乘积\（A \ times B \），当且仅当以下条件之一为时，\（A \ times B \）具有属性\（{\ mathcal {P}} \\） true：两者都\（A \）和\（B \）具有属性\（{\ mathcal {P}} \\），或者\（A \）或\（B \）中的至少一个是向后限制的，这是一种特殊的属性，它控制直接乘积，并且保证所有\（{\ mathcal {P}} \）都成立。