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[[Image:Sphere-wireframe.png|right|thumb|200px|The unit [[sphere]] is an ''algebraic variety'' over the [[real numbers]] because it is the set of all points satisfying the polynomial equation ''x<sup>2</sup> + y<sup>2</sup> +z<sup>2</sup> -1 = 0''.]]
[[Image:Sphere-wireframe.png|right|thumb|200px|The unit [[sphere]] is an ''algebraic variety'' over the [[real numbers]] because it is the set of all points satisfying the polynomial equation ''x<sup>2</sup> + y<sup>2</sup> +z<sup>2</sup> -1 = 0''.]]
An '''algebraic variety''' ''V'' over a [[ring (mathematics)|ring]] ''K'' is defined as the set of all points satisfying a system of polynomial equations with coefficients in ''K''.
An '''algebraic variety''' ''V'' over a [[ring (mathematics)|ring]] ''K'' is defined as the set of all points in ''K'' satisfying a system of polynomial equations with coefficients in ''K''.
[[category:mathematics]]
[[category:mathematics]]