Bourbaki

Exercise 6, § 8

Algebra, X, p. 202

Let II be the set of left ideals of AA. Now prove that dh(A)=sup⁡a∈IdpA(A/a)\mathrm{dh}(A) = \sup_{a \in I} \mathrm{dp}_A(A/a).

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Machine translation of the English, by gpt-5-6. Not checked by a person.