grandes-ecoles 2023 QI.2

grandes-ecoles · France · x-ens-maths-d__mp Groups Subgroup and Normal Subgroup Properties

Let $A$ be a commutative ring. Let $S _ { 1 }$ and $S _ { 2 }$ be two subsets of $A$ such that $S _ { 1 } \subset \mathcal { A } \left( S _ { 2 } \right)$. Show that $\mathcal { A } \left( S _ { 1 } \right) \subset \mathcal { A } \left( S _ { 2 } \right)$.

Let $A$ be a commutative ring. Let $S _ { 1 }$ and $S _ { 2 }$ be two subsets of $A$ such that $S _ { 1 } \subset \mathcal { A } \left( S _ { 2 } \right)$. Show that $\mathcal { A } \left( S _ { 1 } \right) \subset \mathcal { A } \left( S _ { 2 } \right)$.

Paper Questions

QI.1 QI.2 QI.3 QI.4 QI.5 QII.1 QII.2 QII.3 QII.4 QII.5 QIII.1 QIII.2 QIII.3 QIV.1 QIV.2 QIV.3 QV.1 QV.2 QV.3 QV.4