Ivan Shishkin, Rye (1878)

Problems/FieldExerciseUnreviewed

Caractéristique d’un anneau

by FiniteField·
20
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Soit n∈N∗n\in\mathbb{N}^{*}. Déterminer la caractéristique des anneaux AA pour chaque anneau ci-dessous :

  • A=Q.A=\mathbb{Q}.
  • A=Z/nZA=\mathbb{Z}/n\mathbb{Z}.
  • A=(Z/nZ)[X]A=(\mathbb{Z}/n\mathbb{Z})[X].
  • A=(Z/2Z)×(Z/4Z)A=(\mathbb{Z}/2\mathbb{Z})\times (\mathbb{Z}/4\mathbb{Z}).
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