Dobbs, David E.Kiltinen, John O.Orndorff, Bobby J.2017-09-182017-09-181992-01-01David E. Dobbs, John O. Kiltinen, and Bobby J. Orndorff, “Commutative rings with homomorphic power functions,” International Journal of Mathematics and Mathematical Sciences, vol. 15, no. 1, pp. 91-102, 1992. doi:10.1155/S0161171292000103http://hdl.handle.net/10919/79121A (commutative) ring R (with identity) is called m-linear (for an integer m≥2) if (a+b)m=am+bm for all a and b in R. The m-linear reduced rings are characterized, with special attention to the finite case. A structure theorem reduces the study of m-linearity to the case of prime characteristic, for which the following result establishes an analogy with finite fields. For each prime p and integer m≥2 which is not a power of p, there exists an integer s≥m such that, for each ring R of characteristic p, R is m-linear if and only if rm=rps for each r in R. Additional results and examples are given.application/pdfenCreative Commons Attribution 4.0 InternationalArticle - Refereed2017-09-18Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.https://doi.org/10.1155/S0161171292000103