#### cristo

Staff Emeritus

Science Advisor

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What do you mean by the notation ^(V*)?in fact, over more general rings where one cannot always divide, instead of viewing alternating functions as alternating products of linear functions on the module, one views them as linear functions on the exterior module on the original module.

i.e. instead of dfining alternating functions as ^(V*) where V* is linear functions on V, one defines instead ^V, and then alternating fiunctions on (products of) V is defined as linear functions on ^V, i.e. as (^V)*.

the problem is that in general, ^(V*) is not the same as (^V)* i guess.

gee this is something i would like to know about.

V* is the linear functions on V (this is equivalent to the dual space of V, no?). Do you then mean by ^(V*) the alternating functions defined on the dual space V*?

Then for the second case, ^V is defined as the alternating functions on V, and then (^V)* is the dual space of this space of alternating functions?