Spectrum of a Ring
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High Quality Content by WIKIPEDIA articles! Following on from the example, in algebraic geometry one studies algebraic sets, i.e. subsets of Kn (where K is an algebraically closed field) which are defined as the common zeros of a set of polynomials in n variables. If A is such an algebraic set, one considers the commutative ring R of all polynomial functions A K. The maximal ideals of R correspond to the points of A (because K is algebraically closed), and the prime ideals of R correspond to the subvarieties of A (an algebraic set is called irreducible or a variety if it cannot be written as the union of two proper algebraic subsets).…mehr

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High Quality Content by WIKIPEDIA articles! Following on from the example, in algebraic geometry one studies algebraic sets, i.e. subsets of Kn (where K is an algebraically closed field) which are defined as the common zeros of a set of polynomials in n variables. If A is such an algebraic set, one considers the commutative ring R of all polynomial functions A K. The maximal ideals of R correspond to the points of A (because K is algebraically closed), and the prime ideals of R correspond to the subvarieties of A (an algebraic set is called irreducible or a variety if it cannot be written as the union of two proper algebraic subsets).