On the splitting ring of a polynomial

2015/04/04 by Fernando Szechtman, Szechtman, Fernando
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1504.00973

arxiv created 2015/10/16 · arxiv updated 2015/10/19

Abstract

Let f(Z)=Zⁿ-a₁Z^n-1+⋯+(-1)^n-1a_n-1Z+(-1)ⁿa_n be a monic polynomial with coefficients in a ring~R with identity, not necessarily commutative. We study the ideal I_f of R[X₁,…,X_n] generated by σ_i(X₁,…,X_n)-a_i, where σ₁,…,σ_n are the elementary symmetric polynomials, as well as the quotient ring R[X₁,…,X_n]/I_f.

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