# Tag Info

### Characterize rings $R$, such that the countable product $P=R^N$ has the property that every finitely generated submodule of $P$ is free

I think your condition is equivalent to being a semifir (but see the remark below). See Chapter 2 of Paul Cohn, "Free ideal rings and localization in general rings". A commutative semifir is ...
• 13.6k

### Characterize rings $R$, such that the countable product $P=R^N$ has the property that every finitely generated submodule of $P$ is free

Assuming rings are commutative with unity, these are exactly the Bézout domains (and the zero ring). Let $R$ be a non-zero ring. The following are equivalent: $R$ is a Bézout domain (a domain in ...
• 4,666
Accepted

### A commutative ring with unity which does not have relatively pseudo-injective ideals with zero intersection

Can we find a commutative ring $𝑅$ with unity such that there exist two ideals $A, B\subseteq R$ such that $A\cap B=0$ and $𝐴_𝑅$ is NOT pseudo-$𝐵_𝑅$-injective? Let $R=\mathbb Z[x,y]/(x^2,xy,y^2)$,...
• 12.7k