Definition talk:Minimal Polynomial

In the part "Also see", that theorems that are supposed to be proved are part of the definition. I'm not an expert in this area of mathematics, but I think the definition can be weakened. --Dan232 02:15, 23 August 2011 (CDT)

Minimal
Should it not be part of the definition that $\mu \left(x\right)$ is of least possible degree? -- TheSpleen (talk) 11:54, 11 September 2013 (UTC)


 * No, for this follows from the "irreducible" property. But I agree that the definition you propose should be documented, as it is used on Minimal Polynomial is Irreducible. We could also algebraically define it as the unique generator of the ideal $\operatorname{Ann}(\alpha)$ of polynomials $p$ with $p(\alpha)=0$ (since polynomial rings in one variable are PIDs); all three are equivalent. &mdash; Lord_Farin (talk) 15:22, 11 September 2013 (UTC)