Written exam MPRI 2 - 6 , year 2013 – 2014
نویسنده
چکیده
The only documents allowed are your own printed copy of the course slides and your personal notes. The use of electronic devices (computers, phones) is prohibited. The questions are written in English. You can answer either in English or French. The different parts in this exam are independent and can be solved in any order. It will not be answered to any question during the exam. In case of ambiguity or incorrectness in the definitions or questions, it is part of the exam to correct them and answer to the best of your abilities.
منابع مشابه
Written exam MPRI 2 - 6 , year 2014 – 2015
αU (R) ⊆ R] ⇐⇒ { (ρ, a(i)) | (ρ, a) ∈ R, i ∈ [0, ρ(N)− 1] } ⊆ R] ⇐⇒ ∀(ρ, a) ∈ R : ∀i ∈ [0, ρ(N)− 1] : (ρ, a(i)) ∈ R] ⇐⇒ (ρ, a) ∈ R =⇒ ∀i ∈ [0, ρ(N)− 1] : (ρ, a(i)) ∈ R] ⇐⇒ R ⊆ { (ρ, a) | ∀i ∈ [0, ρ(N)− 1] : (ρ, a(i)) ∈ R] } ⇐⇒ R ⊆ γU (R]) Actually, we have a Galois embedding as αU is onto: any (ρ, x) ∈ EU is the abstraction αU ({ (ρ, a) }) of some (ρ, a) ∈ E such that ∀i ∈ [0, ρ(N)− 1] : a(i) = x.
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