It's been awhile since I studied ring theory but here's a question about it:(adsbygoogle = window.adsbygoogle || []).push({});

Let R = C[x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}, x_{8}] be a complex polynomial ring in 8 variables.

Let

f_{1}= x_{1}x_{3}+x_{5}x_{7}and

f_{2}= x_{2}x_{4}+x_{6}x_{8}.

How do [itex]\bar{f}[/itex]_{1}, [itex]\bar{f}[/itex]_{2}in (f_{1},f_{2})R/(x_{1},x_{2})R look like?

Is it

[itex]\bar{f}[/itex]_{1}= x_{5}x_{7}+ (x_{1},x_{2})

[itex]\bar{f}[/itex]_{2}= x_{6}x_{8}+ (x_{1},x_{2})

or is it

[itex]\bar{f}[/itex]_{1}= x_{1}x_{3}+ x_{5}x_{7}+(x_{1},x_{2})

[itex]\bar{f}[/itex]_{2}= x_{2}x_{4}+ x_{6}x_{8}+ (x_{1},x_{2})?

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# Some basic question about a quotient ring

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