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On distributively generated near-rings1
Published online by Cambridge University Press: 20 January 2009
Extract
The following theorems in ring theory are well-known:
1. Let R be a ring. If e is a unique left identity, then e is also a right identity.
2. If R is a ring with more than one element such that aR = R for every nonzero element a ε R, then R is a division ring.
3. A ring R with identity e ≠ 0 is a division ring if and only if it has no proper right ideals.
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- Copyright © Edinburgh Mathematical Society 1969
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