Suppose $M$ and $N$ are free $R$-module($R$ is a commutative ring). The tensor product of $M\otimes_R N$ is free $R$-module? I know for projective modules it is true. How should we build its basis?
2026-03-29 06:28:42.1774765722
Tensor product of free modules
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$$[\bigoplus\limits_{i} R] \otimes_R [ \bigoplus\limits_j R] \cong \bigoplus\limits_{i,j} R \otimes_R R \cong \bigoplus\limits_{i,j} R$$