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In mathematics, the **irrelevant ideal** is the ideal of a graded ring generated by the homogeneous elements of degree greater than zero. More generally, a homogeneous ideal of a graded ring is called an **irrelevant ideal** if its radical contains the irrelevant ideal.^{[1]}

The terminology arises from the connection with algebraic geometry. If *R* = *k*[*x*_{0}, ..., *x _{n}*] (a multivariate polynomial ring in

**^**Zariski & Samuel 1975, §VII.2, p. 154**^**Hartshorne 1977, Exercise I.2.4**^**Hartshorne 1977, §II.2

- Sections 1.5 and 1.8 of Eisenbud, David (1995),
*Commutative algebra with a view toward algebraic geometry*, Graduate Texts in Mathematics, vol. 150, Berlin, New York: Springer-Verlag, ISBN 978-0-387-94269-8, MR 1322960 - Hartshorne, Robin (1977),
*Algebraic Geometry*, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157 - Zariski, Oscar; Samuel, Pierre (1975),
*Commutative algebra volume II*, Graduate Texts in Mathematics, vol. 29 (Reprint of the 1960 ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-90171-8, MR 0389876