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laletrazeta.bsky.social
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10 days ago
I'm not sure I understand the difference between both statements. Can you show an element that is in one ring but not the other?
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totientquotient.bsky.social
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10 days ago
X1+X2+X3+X4+...
is not an element of the polynomial ring
K[X1,X2,X3,X4,...]
because there's infinitely many linearly-independent (over K) terms. But it's an element of the other ring in question since all of the terms have finite degree.
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laletrazeta.bsky.social
•
10 days ago
Ah, I see. This ring appears when studying symmetric functions, which are analogues of symmetric polynomials in it.
You can realize it as the inverse limit of polynomial rings in the category of *graded* rings
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is not an element of the polynomial ring
K[X1,X2,X3,X4,...]
because there's infinitely many linearly-independent (over K) terms. But it's an element of the other ring in question since all of the terms have finite degree.
You can realize it as the inverse limit of polynomial rings in the category of *graded* rings