Commutative algebra Graded rings and filtrations Concept
Homogeneous ideal
Summary
A homogeneous ideal of a graded ring is an ideal that contains all homogeneous components of each of its elements. Equivalently, it is generated by homogeneous elements. Homogeneous ideals of a polynomial ring are the ideals that define subsets of projective space. The quotient by a homogeneous ideal is again graded.
Further reading
About this page
| Tag | 6ZBNGS0P98 |
|---|---|
| URI | m2://6ZBNGS0P98 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 13A02, 13A15 |
| Specializes | Ideal |
| Changed | 2 November 2026 |
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