Homogeneous prime ideals of height h have at most h² quadratic minimal generators, and this bound is sharp as some such primes are minimally generated by exactly h² quadrics.
Eisenbud.Commutative algebra, volume 150 ofGraduate Texts in Mathematics
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Implicit operations are partial functions on algebras defined by first-order formulas and preserved by homomorphisms; the paper develops their algebraic theory.
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Quadratic linear strands of prime ideals
Homogeneous prime ideals of height h have at most h² quadratic minimal generators, and this bound is sharp as some such primes are minimally generated by exactly h² quadrics.
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The theory of implicit operations
Implicit operations are partial functions on algebras defined by first-order formulas and preserved by homomorphisms; the paper develops their algebraic theory.