Talk:Von Neumann regular ring
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I think these things may sometimes be called "absolutely flat" in the commutative case. See Atiyah/MacDonald, Introduction to Commutative Algebra, p. 35. - Gauge 06:10, 7 February 2006 (UTC)
"Generalizations" are not so
[edit]I see that in the section "Generalizations" is placed the notion of "strongly regular", which is in fact not a generalization, but a specialization!
Every strongly regular ring is a von Neumann regular ring, and not the converse.
Actual generalizations of von Neumann regular rings are:
- pi-regular rings.
- PP rings.
- Generalized PP rings.
- CPP rings.
- CPF rings.
- APP rings.
- P-von Neumann regular rings.
Every von Neumann regular ring is contained in those classes.
---Jose Brox —Preceding unsigned comment added by 80.58.205.50 (talk) 17:03, 5 February 2010 (UTC)
Agreed! Shall we change it to "Generalizations and specializations" and be clear in the text which is which? I'm going to change it a bit right now, and I'll let someone else deal with generalizations. Of those, I'm familiar with PP rings and pi-regular rings, but the rest might be too obscure. Good fodder for future discussion.Rschwieb (talk) 19:55, 5 October 2010 (UTC)