Document Type : Research Paper

**Author**

Department of Mathematics, Morgan State University, Baltimore, MD 21251, United States of America

**Abstract**

Let A, B, C, and D be posets. Assume C and D are finite with a greatest element. Also assume that A^{C} ≅B ^{D}. Then there exist posets E, X, Y , and Z such that A ≅E ^{X}, B ≅E ^{Y} , 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.

**Keywords**

**Main Subjects**

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August 2023

Pages 1-27