Commutative rings with homomorphic power functions
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171292000103 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |