New characterizations of Von Neumann regular rings and a conjecture of Shamsuddin
- Autores: Carl Faith
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 40, Nº 2, 1996, págs. 383-385
- Idioma: inglés
- DOI: 10.5565/publmat_40296_09
- Títulos paralelos:
- Nuevas caracterizaciones de los anillos regulares de Von Neumann y una conjetura de Shamsuddin
- Enlaces
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Resumen
A theorem of Utumi states that if $R$ is a right self-injective ring such that every maximal ideal has nonzero annihilator, then $R$ modulo the Jacobson radical $J$ is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when $R$ itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.
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