Talk:Von Neumann regular ring

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)[reply]

"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)[reply]

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)[reply]