nLab
monic polynomial

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Definition

Given a unital ring kk, a monic polynomial over kk is a polynomial with coefficients in kk, whose highest order coefficient is 11.

A root of a monic polynomial over kk is by definition an algebraic integer over kk.

Here algebraic integer usually means algebraic integer over Z\mathbf{Z}. All algebraic integers form a field called the integral closure of Z\mathbf{Z} in C\mathbf{C}.

On the other hand, for a number field KK, an integer in KK is an algebraic integer over Z\mathbf{Z} which is in KK; all integers in KK form a ring of integers 𝒪 K\mathcal{O}_K of the number field KK.

References

Revised on October 2, 2012 12:58:56 by Urs Schreiber (131.174.41.94)