Commutative rings with homomorphic power functions
1992 ◽
Vol 15
(1)
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pp. 91-102
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A (commutative) ringR(with identity) is calledm-linear (for an integerm≥2) if(a+b)m=am+bmfor allaandbinR. Them-linear reduced rings are characterized, with special attention to the finite case. A structure theorem reduces the study ofm-linearity to the case of prime characteristic, for which the following result establishes an analogy with finite fields. For each primepand integerm≥2which is not a power ofp, there exists an integers≥msuch that, for each ringRof characteristicp,Rism-linear if and only ifrm=rpsfor eachrinR. Additional results and examples are given.
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2014 ◽
Vol 14
(01)
◽
pp. 1550008
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Keyword(s):
2013 ◽
Vol 12
(04)
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pp. 1250199
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2011 ◽
Vol 10
(04)
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pp. 665-674
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2007 ◽
Vol 17
(03)
◽
pp. 527-555
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2012 ◽
Vol 12
(03)
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pp. 1250179
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