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Ben McKay
Ben McKay
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I have a question,

Let R$R$ be a ring, and for every R$R$-module M$M$, suppose that we have the following condition:

If M$M$ is cogenerated by any finitely generated $R$-module N$N$, then M$M$ embeds in a finite direct sum of copies of N$N$.

Does this assumption impliesimply that R$R$ is right Artinian?

Thank you for your comments on this question,

I have a question,

Let R be a ring, and for every R-module M, we have the following condition:

If M is cogenerated by any finitely generated $R$-module N, then M embeds in a finite direct sum of copies of N.

Does this assumption implies that R is right Artinian?

Thank you for your comments on this question,

Let $R$ be a ring, and for every $R$-module $M$, suppose that we have the following condition:

If $M$ is cogenerated by any finitely generated $R$-module $N$, then $M$ embeds in a finite direct sum of copies of $N$.

Does this assumption imply that $R$ is right Artinian?

added top-level tag; http://meta.mathoverflow.net/questions/1457/why-are-mo-tags-formatted-as-they-are
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edit approved Aug 2, 2017 at 6:42
Martin Sleziak
edit approved Aug 2, 2017 at 6:42
Martin Sleziak
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Najmeh Dehghani
Najmeh Dehghani
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On Artinian rings

I have a question,

Let R be a ring, and for every R-module M, we have the following condition:

If M is cogenerated by any finitely generated $R$-module N, then M embeds in a finite direct sum of copies of N.

Does this assumption implies that R is right Artinian?

Thank you for your comments on this question,