This is a simple question about notation: Given two generators $x,y$ how does one denote the vector space spanned by all finite **K**-polynomials in $x$ and all finite polynomials in $y$. If I use **K\*\*$[x] \oplus$ \**K*\*$[y]$, then I get two copies of \*\*K**. I could just quotient \**K*\*$[x] \oplus$ \**K*\*$[y]$ by \**K*\*$[(1,0)-(0,1)]$, but this seems overly involved. Similarily, I could quotient \**K*\*$[x,y]$ by <$xy,yx$>, but this too seems overly involved. Does any have any ideas?



Notation: Vector space spanned by all finite polynomials in $x$ and all finite polynomials in $y$
If it is clear from context that you are working in the ambient setting of $k[x,y]$, then you can write $k[x] + k[y]$. Otherwise, I would spell it out in words.


