Let L and M be zero-dimensional frames. It is shown that concerning the Banaschewski compactification ζ, a necessary and sufficient condition for the canonically induced frame homomorphism hL,M : ζL ⊕ ζM→ζ(L ⊕ M) to be an isomorphism is given in terms of the tensor product of the rings of all bounded integer-valued continuous functions on L and M, respectively. This provides the integral counterpart of A. Hager’s work (Math. Zeitschr. 92, 210–224, 1966, Section 2.2) in the setting of frames.

中文翻译：

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零维框架的环张量积𝖅L $\mathfrak {Z}L$

设 L 和 M 是零维框架。结果表明，关于 Banaschewski 紧缩 ζ，正则诱导框架同态 hL,M 的充分必要条件是： ζL ⊕ ζM→ζ(L ⊕ M) 是同构的，由环的张量积给出分别为 L 和 M 上的所有有界整数值连续函数。这提供了 A. Hager 的工作（Math. Zeitschr. 92, 210–224, 1966, Section 2.2）在框架设置中的完整对应物。