Plane modules and distributive rings
Let $A$ be a semiprime ring entire over its center. We prove that the following conditions are equivalent: (a) A is a ring distributive from the right (left); (b) w.gl. $\dim (A) ≤ 1$; moreover, if $M$ is an arbitrary prime ideal of the ring $A$, then $A/M$ is a right Ore set.
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5860 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Let $A$ be a semiprime ring entire over its center. We prove that the following conditions are equivalent:
(a) A is a ring distributive from the right (left); (b) w.gl. $\dim (A) ≤ 1$; moreover, if $M$ is an arbitrary prime ideal of the ring $A$, then $A/M$ is a right Ore set. |
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