# Tag Info

## New answers tagged tensor

3 votes

### Proving the graded structure of the tensor algebra from only the universal property

LSpice asked me to expand my old comment into an answer. Let me write $R$ for whatever base commutative ring you are working over, $V$ for your $R$-module, and $TV := T_R V$ for its "tensor ...
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### Proving the graded structure of the tensor algebra from only the universal property

After all of this time I found a simple and direct solution. I can't believe I didn't think of this before: Let $V$ be an $R$-Module and let $T(V)$ be its tensor algebra. Define $T^n(V)$ to be the ...
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