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Q: Results on additive structure of polynomial rings?

DanI've been wondering recently about results for irreducibility that use the "additive structure" of the polynomial ring at hand. For instance, can we say anything about the irreducibility of a sum of two irreducible polynomials that satisfy some conditions? This seems like an additive number theor...

I will point out that the tag (abstract-algebra) is deprecated on MO, see the tag-info. Another thing which is different from Mathematics is the recommendation to use at least one top-level tag. — Martin Sleziak 47 secs ago
As a side note, the question was posted also on Mathematics (several days ago): Additive structure of polynomial rings.
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Q: Additive structure of polynomial rings

DanI've been wondering recently about results for irreducibility that use the "additive structure" of the polynomial ring at hand. For instance, can we say anything about the irreducibility of a sum of two irreducible polynomials that satisfy some conditions? This seems like an additive number theor...

 

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