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Abstract Algebra

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Submodule of a Module over a Field: Polynomials in Two Variables

ABSALG-UI@12F

Which of the following is not a submodule of the $\mathbb{R}$-module $\mathbb{R}[x,y]$ of polynomials in $x$ and $y$?

A

$\mathbb{R}$

B

$\mathbb{R}[x]$

C

$\mathbb{R}[y]$

D

$\mathbb{R}[x,y]\setminus\mathbb{R}[x]$

E

$\mathbb{R}[x+y]$

F

$\mathbb{R}[xy]$