A note on a theorem of Fried and MacRae
The theorem of \textit{M. D. Fried} and \textit{R. E. MacRae} [Ill. J. Math. 13, 165--171 (1969; Zbl 0174.07302), Math. Ann. 180, 220--226 (1969; Zbl 0185.28803)] states that for polynomials \(L,R,l,r\) in several variables over a field \(k\) there exists a univariate polynomial \(H\) over \(k\) with \(L=H(l)\), \(R=H(r)\) iff \(l-r\) divides the polynomial \(L-R\). The authors are able to deduce this from a category theoretical statement: the pushout diagram of stable monos is also a pullback diagram (not in general but in these finitary algebraic categories they consider). As a consequence, with some additional assumptions, the authors can prove a generalized FMR-theorem for rational functions in several variables.
scientific article; zbMATH DE number 815708
scientific article