Algebra II: Chapters 4–7 by Nicolas Bourbaki (auth.)

TS (M) . EL Let AI' A2, ... , An be pairwise distinct elements of L and let XI E M/.. l , xn EM/.... By Prop. ~P 'YPI (XI) ® ... cXn )) = 'Yp(XI + ... + xn) . 49 SYMMETRIC TENSORS AND POLYNOMIAL MAPPINGS Let N be an A-module which is a direct sum of a family (N~)~ E L of submodules. For every A E L let u~ be a homomorphism of M~ into N~. Let u be the homomorphism of Minto N defined by the u~. , ® TS(N;) - h' TS(N) commutes, where hand h' are canonical homomorphisms. For if Z E TS (M~) and if i~ (resp.