if not, then we’ll essentially need another way to define determinant for projective modules because that’s equivalent to defining an alternating map?
There’s a lot of cases in mathematics where two notions can be stated in terms of each other, but it doesn’t tell us which order to define things in.
The only other thought I have is that I have to use the fact that W is projective and finitely generated. This is equivalent to W being dualisable. So the definition is likely to use W∗ somewhere.
There’s a lot of cases in mathematics where two notions can be stated in terms of each other, but it doesn’t tell us which order to define things in.
The only other thought I have is that I have to use the fact that W is projective and finitely generated. This is equivalent to W being dualisable. So the definition is likely to use W∗ somewhere.