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Post Closed as "off topic" by Steven Landsburg, Benjamin Steinberg, Steven Sam, Emil Jeřábek, user9072
edited to make it look more professional and less like shouting
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Todd Trimble
Todd Trimble
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how iLet $R$ be a commutative noetherian ring, and let $M$ be an $R$-module. How I can show that if any localization of M$M_p$ at a prime ideal p$p$ of the ring R is$R$ is injective over $R_p$, then M$M$ is injective?R IS COMMUCATIVE NOETHERIAN RING.

how i can show that if any localization of M at prime ideal p of the ring R is injective then M is injective?R IS COMMUCATIVE NOETHERIAN RING.

Let $R$ be a commutative noetherian ring, and let $M$ be an $R$-module. How I can show that if any localization $M_p$ at a prime ideal $p$ of the ring $R$ is injective over $R_p$, then $M$ is injective?

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sasha
sasha
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injectivity is a local property over noetherian rings

how i can show that if any localization of M at prime ideal p of the ring R is injective then M is injective?R IS COMMUCATIVE NOETHERIAN RING.