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Nov 19, 2010 at 20:00 history edited Dustin Cartwright CC BY-SA 2.5
Fixed condition 1: need to check that $P^{gp}$ is torsion-free, not just $P$
Nov 18, 2010 at 17:33 vote accept unknown
Nov 18, 2010 at 16:18 comment added Dustin Cartwright @Dave, yes, (1) and (2) are exactly what you need for k[P] to be an integral domain, and then having (3) in addition says that it is a normal domain.
Nov 18, 2010 at 16:15 history edited Dustin Cartwright CC BY-SA 2.5
Corrected 3rd point
Nov 18, 2010 at 6:31 comment added Dave Anderson In Condition (3), I think you mean to say $k[P]$ is a normal (i.e., integrally closed) domain. To me, at least, "integral domain" just means no zerodivisors, which is implied by (1) and (2).
Nov 18, 2010 at 5:23 history answered Dustin Cartwright CC BY-SA 2.5