Quasi-unit regularity and $QB$-rings
Some relations for quasiunit regular rings and $QB$-rings, as well as for pseudounit regular rings and $QB_{\infty}$-rings, are obtained. In the first part of the paper, we prove that (an exchange ring $R$ is a $QB$-ring) (whenever $x \in R$ is regular, there exists a quasiunit regular element $w \...
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| Datum: | 2012 |
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| Hauptverfasser: | , , , , , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2586 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Some relations for quasiunit regular rings and $QB$-rings, as well as for pseudounit regular rings and $QB_{\infty}$-rings, are obtained.
In the first part of the paper, we prove that (an exchange ring $R$ is a $QB$-ring) (whenever $x \in R$ is regular, there exists a quasiunit regular element $w \in R$ such that $x = xyx = xyw$ for some $y \in R$) — (whenever $aR + bR = dR$ in $R$,
there exists a quasiunit regular element $w \in R$ such that $a + bz = dw$ for some $z \in R$).
Similarly, we also give necessary and sufficient conditions for $QB_{\infty}$-rings in the second part of the paper. |
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