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Osiris
Osiris
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Consider an integer polynomial ring, $A = \mathbb{Z}[t]$, and a ring of fractions, $B = \mathbb{Z}[t, t^{-1}]$; obviously, $A$ is a subring of $B$.

Now we consider two modules over $A$ and $B$, $M$ and $N$. We want to construct a map from $M$$N$ to $N$$M$. But the question is that the two modules are not over the same polynomial ring. So how can we make it?

Great thanks!

Consider an integer polynomial ring, $A = \mathbb{Z}[t]$, and a ring of fractions, $B = \mathbb{Z}[t, t^{-1}]$; obviously, $A$ is a subring of $B$.

Now we consider two modules over $A$ and $B$, $M$ and $N$. We want to construct a map from $M$ to $N$. But the question is that the two modules are not over the same polynomial ring. So how can we make it?

Great thanks!

Consider an integer polynomial ring, $A = \mathbb{Z}[t]$, and a ring of fractions, $B = \mathbb{Z}[t, t^{-1}]$; obviously, $A$ is a subring of $B$.

Now we consider two modules over $A$ and $B$, $M$ and $N$. We want to construct a map from $N$ to $M$. But the question is that the two modules are not over the same polynomial ring. So how can we make it?

Great thanks!

Post Closed as "not a real question" by Felipe Voloch, J.C. Ottem, Kevin Walker, user9072, Andreas Blass
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Todd Trimble
Todd Trimble
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Consider an integer polynomial ring, A=ZZ[t]$A = \mathbb{Z}[t]$, and a quotient ring, B=ZZ[t, t^(-1)] of fractions, obviously $B = \mathbb{Z}[t, t^{-1}]$; obviously, A$A$ is a subring of B$B$.

Now we consider two modules over A$A$ and B$B$, A^1和B^1$M$ and $N$. We want to construct a map from A^1$M$ to B^1$N$. But the question is that the two modules are not over the same polynomial ring. So how can we make it?

Great thanks!

Consider an integer polynomial ring, A=ZZ[t], and a quotient ring, B=ZZ[t, t^(-1)], obviously, A is a subring of B.

Now we consider two modules over A and B, A^1和B^1. We want to construct a map from A^1 to B^1. But the question is that the two modules are not over the same polynomial ring. So how can we make it?

Great thanks!

Consider an integer polynomial ring, $A = \mathbb{Z}[t]$, and a ring of fractions, $B = \mathbb{Z}[t, t^{-1}]$; obviously, $A$ is a subring of $B$.

Now we consider two modules over $A$ and $B$, $M$ and $N$. We want to construct a map from $M$ to $N$. But the question is that the two modules are not over the same polynomial ring. So how can we make it?

Great thanks!

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Osiris
Osiris
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Question about modules, quotient rings, and polynomial rings?

Consider an integer polynomial ring, A=ZZ[t], and a quotient ring, B=ZZ[t, t^(-1)], obviously, A is a subring of B.

Now we consider two modules over A and B, A^1和B^1. We want to construct a map from A^1 to B^1. But the question is that the two modules are not over the same polynomial ring. So how can we make it?

Great thanks!