Ivan Shishkin, Rye (1878)

Problems/RingExerciseUnreviewed

On peut perdre en divisant

by FiniteField·
35
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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  1. Soit AA un anneau intègre et SS une partie multiplicative ne contenant pas 00. Montrer que l’application canonique ℓS ⁣:A→S−1A\ell_{S}\colon A\to S^{-1}A est injective.
  2. Montrer que S={ 3 }S=\set{3} est multiplicative dans A=Z/6ZA=\mathbb{Z}/6\mathbb{Z} et montrer que S−1A≃Z/2Z.S^{-1}A\simeq \mathbb{Z}/2\mathbb{Z}.
  3. L’application ℓS\ell_{S} est-elle toujours injective ?
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