= Reduced norm
{title2=$\operatorname{Nrd}_{A/K}:A\to K$}
The <reduced norm> of an element of a <central simple algebra> of degree $d$ is its <determinant> after any splitting isomorphism to $M_d$. <Inner automorphisms of a matrix algebra> preserve that <determinant>, while Galois invariance descends its polynomial coefficients to the center. It is a multiplicative homogeneous degree-$d$ polynomial, vanishing exactly on noninvertible elements. On a <central division algebra> it is anisotropic.
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