Do we have $a\otimes 1=0$ if and only if $a=0$?

by Born to be proud   Last Updated June 13, 2019 12:20 PM

Let $S$ be a commutative ring with $1\neq 0$ and $M$ any abelian group. For any $a\otimes 1\in M\otimes_{\Bbb Z}S$, do we have $a\otimes 1=0$ if and only if $a=0$?



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