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Luc Guyot
Luc Guyot
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In this question, all rings are commutative with a 1$1$, unless we explicitly say so, and all morphisms of rings send 1$1$ to 1$1$.

Let A$A$ be a Noetherian local integral domain. Let T$T$ be a non-zero A$A$-algebra which, as an A-module, is finitely-generated and torsion-free.

Can one realise T$T$ as a subring of the (not necessarily commutative) ring End_A(A^n)$End_A(A^n)$ for some n>=1$n \ge 1$?

In this question, all rings are commutative with a 1, unless we explicitly say so, and all morphisms of rings send 1 to 1.

Let A be a Noetherian local integral domain. Let T be a non-zero A-algebra which, as an A-module, is finitely-generated and torsion-free.

Can one realise T as a subring of the (not necessarily commutative) ring End_A(A^n) for some n>=1?

In this question, all rings are commutative with a $1$, unless we explicitly say so, and all morphisms of rings send $1$ to $1$.

Let $A$ be a Noetherian local integral domain. Let $T$ be a non-zero $A$-algebra which, as an A-module, is finitely-generated and torsion-free.

Can one realise $T$ as a subring of the (not necessarily commutative) ring $End_A(A^n)$ for some $n \ge 1$?

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Kevin Buzzard
Kevin Buzzard
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Which rings are subrings of matrix rings?

In this question, all rings are commutative with a 1, unless we explicitly say so, and all morphisms of rings send 1 to 1.

Let A be a Noetherian local integral domain. Let T be a non-zero A-algebra which, as an A-module, is finitely-generated and torsion-free.

Can one realise T as a subring of the (not necessarily commutative) ring End_A(A^n) for some n>=1?