- #1
mathmari
Gold Member
MHB
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Hey! ![Eek! :eek: :eek:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Let $R$ be a commutative ring with unit.
Let $T$ be a linear mapping from $\mathbb{R}^2$ to $\mathbb{R}^2$ that is given by the projection at the $y$-axis.
I want to show that the only $\mathbb{R}[x]$-submodule (as for the action that $T$ defines) of $\mathbb{R}^2$ are $\mathbb{R}^2$, $0$, $x$-axis and $y$-axis.
Could you give me some hints how we could show that? (Wondering)
Let $R$ be a commutative ring with unit.
Let $T$ be a linear mapping from $\mathbb{R}^2$ to $\mathbb{R}^2$ that is given by the projection at the $y$-axis.
I want to show that the only $\mathbb{R}[x]$-submodule (as for the action that $T$ defines) of $\mathbb{R}^2$ are $\mathbb{R}^2$, $0$, $x$-axis and $y$-axis.
Could you give me some hints how we could show that? (Wondering)