Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585319120230801Cancel culture12710358010.48308/cgasa.19.1.1ENJonathan DavidFarleyDepartment of Mathematics, Morgan State University, Baltimore, MD 21251, United States of AmericaJournal Article20230610Let A, B, C, and D be posets. Assume C and D are finite with a greatest element. Also assume that A<sup>C</sup> ≅B <sup>D</sup>. Then there exist posets E, X, Y , and Z such that A ≅E <sup>X</sup>, B ≅E <sup>Y</sup> , C≅Y ×Z, and D≅X×Z. If C≅D, then A≅B. This generalizes a theorem of Jónsson and McKenzie, who proved it when A and B were meet-semilattices.https://cgasa.sbu.ac.ir/article_103580_7e019629f987fc8498db5f7b71403816.pdf