Geodesic
On Division Near-Rings
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1366-1371

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

The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if for every a ≠0 in R, there exists a unique b in R such that aba = a.(B) Let R be a near-ring which contains a right identity e ≠ 0. Then R is adivision near-ring if and only if it contains no proper R-subgroups.(C) Let R be a finite near-ring with identity. Then R is a division near-ringif and only if the R-module R+ is simple.In this paper we will show that (A) can be generalized to distributively generated near-rings. We also will extend (B) and (C) to a larger class of near-rings. 
Ligh, Steve. On Division Near-Rings. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1366-1371. doi: 10.4153/CJM-1969-151-5
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