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Commutative rings with homomorphic power functions

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  • David E. Dobbs
  • John O. Kiltinen
  • Bobby J. Orndorff

Abstract

A (commutative) ring R (with identity) is called m -linear (for an integer m ≥ 2 ) if ( a + b ) m = a m + b m 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 r m = r p s for each r in R . Additional results and examples are given.

Suggested Citation

  • David E. Dobbs & John O. Kiltinen & Bobby J. Orndorff, 1992. "Commutative rings with homomorphic power functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 15, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:706475
    DOI: 10.1155/S0161171292000103
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