Geodesic
A Commutativity Theorem for Near-Rings
Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 25-28

Voir la notice de l'article provenant de la source Cambridge University Press

A ring or near-ring R is called periodic if for each xεR, there exist distinct positive integers n, m for which xn = xm . A well-known theorem of Herstein states that a periodic ring is commutative if its nilpotent elements are central [5], and Ligh [6] has asked whether a similar result holds for distributively-generated (d-g) near-rings. It is the purpose of this note to provide an affirmative answer. 
Bell, Howard E. A Commutativity Theorem for Near-Rings. Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 25-28. doi: 10.4153/CMB-1977-004-5
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[1] 1. Bell, H. E., Near-rings in which each element is a power of itself, Bull. Australian Math. Soc. 2 (1970), 363-368. Google Scholar

[2] 2. Bell, H. E., Certain near-rings are rings, J. London Math. Soc. (2) 4 (1971), 264-270. Google Scholar

[3] 3. Chacron, M., On a theorem of Herstein, Canadian J. Math. 21 (1969), 1348-1353. Google Scholar

[4] 4. Fröhlich, A., Distributively-generated near-rings, I, Ideal theory, Proc. London Math. Soc. (3) 8, (1958), 76-94. Google Scholar

[5] 5. Herstein, I. N., A note on rings with central nilpotent elements, Proc. Amer. Math. Soc. 5 (1954), 620. Google Scholar

[6] 6. Ligh, S., Some commutativity theorems for near-rings, Kyungpook Math. J. 13 (1973), 165-170. Google Scholar

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