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gptkbp:instanceOf
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gptkb:academic
gptkb:mathematical_concept
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gptkbp:notableIdea
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gptkb:Betti_numbers
gptkb:Euclidean_domain
gptkb:Dedekind_domain
gptkb:Hilbert's_Nullstellensatz
gptkb:Zariski_topology
gptkb:Noetherian_ring
gptkb:local_ring
gptkb:reduction
gptkb:spectrum_of_a_ring
gptkb:Artin–Rees_lemma
gptkb:Artin_approximation_theorem
gptkb:Artinian_ring
gptkb:Auslander–Buchsbaum_formula
gptkb:Chinese_remainder_theorem
gptkb:Cohen–Macaulay_ring
gptkb:Eisenbud's_theorem
gptkb:Frobenius_endomorphism
gptkb:Gorenstein_ring
gptkb:Grothendieck_group
gptkb:Hilbert_basis_theorem
gptkb:Hilbert_polynomial
gptkb:Koszul_complex
gptkb:Krull's_principal_ideal_theorem
gptkb:Krull–Schmidt_theorem
gptkb:Krull_dimension
gptkb:Krull_intersection_theorem
gptkb:Matlis_duality
gptkb:Nakayama's_lemma
gptkb:Picard_group
gptkb:Serre's_criterion_for_normality
gptkb:divisor_class_group
gptkb:valuation_ring
gptkb:Jacobson_radical
gptkb:prime_ideal
gptkb:Lasker–Noether_theorem
gptkb:exact_sequence
gptkb:integral_domain
gptkb:principal_ideal_domain
gptkb:unique_factorization_domain
polynomial ring
homomorphism
Fitting ideal
Rees algebra
annihilator
associated prime
canonical module
completion
depth
depth lemma
depth of a module
depth of a ring
dimension theory
finitely generated module
flat module
homological conjectures
homological dimension
injective module
integral closure
integral extension
localization
maximal ideal
minimal prime
power series ring
primary decomposition
projective module
regular local ring
regular sequence
support of a module
syzygy
tensor product
tight closure
valuation
multiplicity
discrete valuation ring
graded module
graded ring
free module
residue field
zero divisor
Bass numbers
Spec of a ring
blowup algebra
chain conditions
determinantal ideal
dimension formula
extension of scalars
faithfully flat module
finitely presented module
fraction field
module over a ring
nilpotent element
torsion module
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gptkbp:relatedTo
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gptkb:algebraic_geometry
algebraic number theory
homological algebra
ring theory
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gptkbp:studies
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algebraic structures
commutative rings
ideals
modules
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gptkbp:bfsParent
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gptkb:Going-down_theorem
gptkb:Going-up_theorem
gptkb:Tor_functor
gptkb:Ideal
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gptkbp:bfsLayer
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6
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https://www.w3.org/2000/01/rdf-schema#label
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Commutative algebra
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