Abstract
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.
Publisher
Cambridge University Press (CUP)
Cited by
6 articles.
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1. On hypernearring of quotients;Communications in Algebra;2023-03-10
2. Division hypernear-rings;Analele Universitatii "Ovidius" Constanta - Seria Matematica;2018-12-01
3. Finite hereditary near-field groups;Monatshefte für Mathematik;1978-03
4. Bibliography;Near-Rings - The Theory and its Applications;1977
5. Some commutativity theorems for rings and near rings;Acta Mathematica Academiae Scientiarum Hungaricae;1976-03