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Let wi and wa be k-forms defined on all of IR". Show that wi and wy have the same exterior derivative, that is, dwi = dw2, %3D if and only if Wi = w2 + dŋ for some (k – 1)-form 7 on R".

Let wi and wa be k-forms defined on all of IR". Show that wi and wy have the same exterior derivative, that is, dwi = dw2, %3D if and only if Wi = w2 + dŋ for some (k – 1)-form 7 on R".

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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Let wj and w2 be k-forms defined on all of R". Show that wi and wa have the same exterior derivative, that is, dwi = dw2, if and only if Wi = w2 + dn for some (k – 1)-form 7 on R".
Transcribed Image Text:Let wj and w2 be k-forms defined on all of R". Show that wi and wa have the same exterior derivative, that is, dwi = dw2, if and only if Wi = w2 + dn for some (k – 1)-form 7 on R".
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