Commutative rings with homomorphic power functions

Autor:	David E. Dobbs, John O. Kiltinen, Bobby J. Orndorff
Jazyk:	angličtina
Rok vydání:	1992
Předmět:	commutative ring m-linear characteristic direct product field Jacobson radical reduced ring. Mathematics QA1-939
Zdroj:	International Journal of Mathematics and Mathematical Sciences, Vol 15, Iss 1, Pp 91-102 (1992)
Druh dokumentu:	article
ISSN:	0161-1712 1687-0425 01611712
DOI:	10.1155/S0161171292000103
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/fe535070b9cc4a0b893a6d3eb8e230b2 Zobrazit plný text záznamu Plný text View record in DOAJ