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edit approved Mar 21, 2015 at 13:38
Dag Oskar Madsen
edit approved Mar 21, 2015 at 13:38
Dag Oskar Madsen
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Injective dimension of cyclic modules.

Let R$R$ be a non-Noetherian ring. Is its left global dimension lD(R) = sup { id(M) | M is a cyclic R-module${\rm{lD}}(R)$ equal to }$\sup \{ {\rm{id}}(M) \mid M \text{ is a cyclic $R$-module} \}$? id(M)Here $\rm{{id}}(M)$ denotes the injective dimension of R$M$.

Injective dimension of cyclic modules.

Let R be a non-Noetherian ring. Is its left global dimension lD(R) = sup { id(M) | M is a cyclic R-module }? id(M) denotes the injective dimension of R.

Injective dimension of cyclic modules

Let $R$ be a non-Noetherian ring. Is its left global dimension ${\rm{lD}}(R)$ equal to $\sup \{ {\rm{id}}(M) \mid M \text{ is a cyclic $R$-module} \}$? Here $\rm{{id}}(M)$ denotes the injective dimension of $M$.

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TmobiusX
TmobiusX
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Injective dimension of cyclic modules.

Let R be a non-Noetherian ring. Is its left global dimension lD(R) = sup { id(M) | M is a cyclic R-module }? id(M) denotes the injective dimension of R.