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Let $R$ be a commutative ring,ring; let $M$, $N$ be $R$-modules and let $f\colon M\to N$ be an injective homomorphism of $R$-modules. Is $f\otimes {\rm id}\colon M\otimes_RN\to N\otimes_RN$ injective?
Let $R$ be a commutative ring, let $M$, $N$ be $R$-modules and let $f\colon M\to N$ be an injective homomorphism of $R$-modules. Is $f\otimes {\rm id}\colon M\otimes_RN\to N\otimes_RN$ injective?
Let $R$ be a commutative ring; let $M$, $N$ be $R$-modules and let $f\colon M\to N$ be an injective homomorphism of $R$-modules. Is $f\otimes {\rm id}\colon M\otimes_RN\to N\otimes_RN$ injective?
Injective homomorphism of modules and tensor product
Let $R$ be a commutative ring, let $M$, $N$ be $R$-modules and let $f\colon M\to N$ be an injective homomorphism of $R$-modules. Is $f\otimes {\rm id}\colon M\otimes_RN\to N\otimes_RN$ injective?
