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References to 'join irreducibility'
1. All unnatural square roots are irrational by ubershmekel
2. composite number by mathcam
3. Galois group of a quartic polynomial by rm50
4. hyperk\"ahler manifold by tiphareth
5. Kurosh-Ore theorem by CWoo
6. representation theory of $\mathfrak{sl}_2 \mathbb{C}$ by benjaminfjones
7. splitting field of a finite set of polynomials by polarbear
8. thin algebraic set by alozano