grandes-ecoles 2023 QI.4

grandes-ecoles · France · x-ens-maths-d__mp Groups Ring and Field Structure
Show that if $n$ is a strictly positive integer, the ring $\mathbf { Z } \left[ X _ { 1 } , \ldots , X _ { n } \right]$ has property (TF), but not property (F). 
Show that if $n$ is a strictly positive integer, the ring $\mathbf { Z } \left[ X _ { 1 } , \ldots , X _ { n } \right]$ has property (TF), but not property (F).
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