Commutative rings with homomorphic power functions

Dobbs, David E.; Kiltinen, John O.; Orndorff, Bobby J.

Commutative rings with homomorphic power functions

dc.contributor.author	Dobbs, David E.	en
dc.contributor.author	Kiltinen, John O.	en
dc.contributor.author	Orndorff, Bobby J.	en
dc.contributor.department	Mathematics	en
dc.date.accessioned	2017-09-18T10:12:15Z	en
dc.date.available	2017-09-18T10:12:15Z	en
dc.date.issued	1992-01-01	en
dc.date.updated	2017-09-18T10:12:15Z	en
dc.description.abstract	A (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.	en
dc.description.version	Published version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	David 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/S0161171292000103	en
dc.identifier.doi	https://doi.org/10.1155/S0161171292000103	en
dc.identifier.uri	http://hdl.handle.net/10919/79121	en
dc.language.iso	en	en
dc.publisher	Hindawi	en
dc.rights	Creative Commons Attribution 4.0 International	en
dc.rights.holder	Copyright © 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.	en
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	en
dc.title	Commutative rings with homomorphic power functions	en
dc.title.serial	International Journal of Mathematics and Mathematical Sciences	en
dc.type	Article - Refereed	en
dc.type.dcmitype	Text	en