A study on near-rings with semi-central idempotents. (Q2800451)
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scientific article; zbMATH DE number 6569524
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A study on near-rings with semi-central idempotents. |
scientific article; zbMATH DE number 6569524 |
Statements
15 April 2016
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reduced near-rings
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regular near-rings
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semi-central idempotents
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0.9422492
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0.9378995
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A study on near-rings with semi-central idempotents. (English)
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This short paper should be read with care. McCoy (center of p. 760) proved his result for rings, not for near-rings. It is clear that ``reversible'' implies ``zero-symmetric''. Lemma 1 requires ``zero-symmetric'', so \(0b=0\). In Lemma 2, again \(0a=0\), so Lemma 2 is trivial. In Proposition 3, the assumptions of Lemmata 1 and 2 are missing; so it is doubtful if this Proposition is correct and can be used in the proof of Proposition 6. Since ``reduced'' implies ``reversible'', the assumption ``Let \(R\) be a reversible reduced near-ring'' in Proposition 8 sounds strange.
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