I-smoothness and regularity

I'm reading Matsumura's Commutative ring theory and in chapter 11 he proves that if A is a noetehrian complete local k-algebra (k a field), then if A is m-smooth over k (m the maximal ideal of A), then A is a regular ring. Is it true that m-smoothness implies regularity when A is just a noetherian complete local ring and does not contain any field? thank you.

flag	asked Dec 2 2010 at 22:24 xi 1

	m-smoothness over what? – Graham Leuschke Dec 3 2010 at 2:48
	m-smoothness over Z for example, or if A is an R-algebra over R. – xi Dec 4 2010 at 4:01