# Tag Info

### Gorenstein projective module over commutative local algebras

Regarding Question 2, if a local ring has finitely many indecomposable Gorenstein projective modules, and at least one non-free, then the ring must have isolated singularity and must be an abstract ...

### Equivalences of categories of complexes of modules

The answer is yes by the same type of Morita theory, namely $Z(Ch(R))\cong R$, where $Z(A)$ is $End(id_A)$, the ring of endomorphisms of an abelian category EDIT : sorry, I hadn't seen that you were ...
Accepted

### Topological modules over a locally compact ring

Not necessarily. Start from $A=\mathbf{R}[t]/(t^2)$ and $R$ its closed cocompact unital subring $\{a+bt:a\in\mathbf{Z},b\in\mathbf{R}\}$. Write $J=tA$. Then every additive subgroup of $R^2$ contained ...
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### $k(F_i)_{i=1}^{n}=k(G_j)_{j=1}^{m}$ iff there exist $a_i,b_j \in k$ such that $\langle F_i-a_i \rangle_{i=1}^{n} = \langle G_j-b_j \rangle_{j=1}^{m}$

If $F_1 = 1$ and $G_1 = x,G_2 = x+1$, we have $(F_1 - 0) = (G_1 - 0, G_2 - 0)$ are both the trivial ideal $(1) = \mathbb{C}[x, y]$.
### Double dual of free $\mathbb{Z}_{(p)}$-modules
E. E. Enochs, “A note on reflexive modules”, Pacific J. Math. 14 (1964), 879–881 shows that, over a discrete valuation ring $R$, the free module with denumerable base is reflexive (meaning that the ...