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Displaying similar documents to “Hausdorff compactifications of completely regular spaces”

On clean ideals.

Chen, Huanyin, Chen, Miaosen (2003)

International Journal of Mathematics and Mathematical Sciences

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New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.

Carl Faith (1996)

Publicacions Matemàtiques

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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.