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From: shirker on 15 Dec 2009 07:40
I need some help with a problem from Dummit and Foote, Chapter 11.5#8c:

"8c) Give an example of an integral domain R and an R-module I in F [F = the field of fractions of R] with Lambda^i(I) /= 0 for each i>=0. [i.e. the ith exterior power of I as an R-module is nonzero for each i>=0] (c.f. example following Corollary 37)."

The referenced example proves that if R=Z[x,y] and I=(x,y), then the 2nd exterior power of I is nonzero. It's proved by showing that the map (ax+by,cx+dy)-> ad-bc mod (x,y) is a well-defined nonzero bilinear alternating map from IxI to R/I. (The a,b,c,d above are polynomials).

Thanks in advance.
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