In mathematics, the irrelevant ideal is the ideal of a graded ring generated by the homogeneous elements of degree greater than zero.
[1] The terminology arises from the connection with algebraic geometry.
If R = k[x0, ..., xn] (a multivariate polynomial ring in n+1 variables over an algebraically closed field k) is graded with respect to degree, there is a bijective correspondence between projective algebraic sets in projective n-space over k and homogeneous, radical ideals of R not equal to the irrelevant ideal.
[2] More generally, for an arbitrary graded ring R, the Proj construction disregards all irrelevant ideals of R.[3]
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