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Another problem of Jónsson and McKenzie from 1982: refinement properties for connected powers of posets
Algebra universalis ( IF 0.6 ) Pub Date : 2021-07-19 , DOI: 10.1007/s00012-020-00698-y
Jonathan David Farley 1
Affiliation  

It is proven in this note that if non-empty posets A, B, C, and D satisfy \(A^C\cong B^D\) where C, D, and \(A^C\) are finite and connected, then there exist posets E, X, Y, and Z such that \(A\cong E^X\), \(B\cong E^Y\), \(C\cong Y\times Z\), and \(D\cong X\times Z\). This solves a problem posed by Jónsson and McKenzie in 1982.



中文翻译:

1982 年 Jónsson 和 McKenzie 的另一个问题:偏序集连接幂的细化属性

本笔记证明,如果非空位组ABCD满足\(A^C\cong B^D\)其中CD\(A^C\)是有限且连通的,则存在偏序EXYZ使得\(A\cong E^X\)\(B\cong E^Y\)\(C\cong Y\times Z\)\(D\cong X\times Z\)。这解决了 Jónsson 和 McKenzie 在 1982 年提出的问题。

更新日期:2021-07-19
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