# Ring detail

## Name: Goodearl's simple self-injective von Neumann regular ring

Description: Let $L$ be an irreducible continuous geometry in case $\infty$ (i.e. fails the DCC) as constructed in von Neumann's Examples of Continuous Geometries. The ring resulting from von Neumann's coorditanization theorem is the required ring.

Reference(s):

• K. Goodearl. Simple self-injective rings need not be artinian. (1974) @ Example 1 p 86

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• = has the property
• = does not have the property
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