Affine ring: Difference between revisions
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==Definition== | ==Definition== | ||
Let <math>R</math> be a [[commutative unital ring]]. An '''affine ring''' over <math>R</math> is a ring isomorphic to <math>R[x_1,x_2 | Let <math>R</math> be a [[commutative unital ring]]. An '''affine ring''' over <math>R</math> is a ring isomorphic to <math>R[x_1,x_2,\ldots,x_n]/I</math> where <math>I</math> is an [[ideal]]. | ||
When we simply say '''affine ring''', we may mean [[affine ring over a field]], viz affine ring where the ring <math>R</math> is a field. | When we simply say '''affine ring''', we may mean [[affine ring over a field]], viz affine ring where the ring <math>R</math> is a field. | ||
Latest revision as of 16:18, 12 May 2008
Definition
Let be a commutative unital ring. An affine ring over is a ring isomorphic to where is an ideal.
![{\displaystyle R[x_{1},x_{2},\ldots ,x_{n}]/I}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1fd7ccd5121bfc230b1d1793df32ec8ca952c6b)
When we simply say affine ring, we may mean affine ring over a field, viz affine ring where the ring is a field.
Facts
An affine ring over an affine ring is also an affine ring over the base field.