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June 8th, 2017, 12:03 PM   #11
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No, no, we aren't talking about rings of formal power series. I meant field of rational functions. Sorry. :<
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Originally Posted by Maschke
Coefficients of what?
Polynomials.
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Originally Posted by Maschke
Of what ring?
Of field of rational functions.
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Originally Posted by Maschke
Is this a ring of formal power series? Where did that come from?
It's just 1 interpreted as polynomial of zero degree. I just thought it would be better to write it this way instead of typing only 1.

Is everything clear now?
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June 8th, 2017, 12:09 PM   #12
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Originally Posted by IAmABread View Post
No, no, we aren't talking about rings of formal power series. I meant field of rational functions. Sorry. :<
Polynomials.Of field of rational functions.It's just 1 interpreted as polynomial of zero degree. I just thought it would be better to write it this way instead of typing only 1.

Is everything clear now?
Well now that you say you're talking about the field of rational functions, yes, 1 is the multiplicative identity. And since 1 + 1 + 1 = 0 this field has characteristic 3. That was ABVictor's point earlier.

Last edited by Maschke; June 8th, 2017 at 12:14 PM.
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June 8th, 2017, 12:18 PM   #13
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Okay, thank you all kindly.
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June 8th, 2017, 12:27 PM   #14
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Okay, thank you all kindly.
Glad that was helpful. ABVictor's example of rational functions is much more concrete than my idea of using algebraic closures, since the latter are quite murky even though they do exist.

If you are interested in finite fields you should see if you can work out the field of four elements.
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