Statements (109)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:academic
gptkb:mathematical_concept |
| https://www.w3.org/2000/01/rdf-schema#label |
Commutative algebra
|
| gptkbp:notableIdea |
gptkb:Betti_numbers
gptkb:Dedekind_domain gptkb:Hilbert's_Nullstellensatz gptkb:Zariski_topology 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:Lasker–Noether_theorem Noetherian ring polynomial ring Euclidean domain 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 domain integral extension local ring localization maximal ideal minimal prime power series ring primary decomposition principal ideal domain projective module reduction regular local ring regular sequence spectrum of a ring support of a module syzygy tensor product tight closure unique factorization domain valuation multiplicity discrete valuation ring graded module graded ring exact sequence free module prime ideal 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 |
| gptkbp:relatedTo |
gptkb:algebraic_geometry
algebraic number theory homological algebra ring theory |
| gptkbp:studies |
algebraic structures
commutative rings ideals modules |
| gptkbp:bfsParent |
gptkb:Going-down_theorem
gptkb:Going-up_theorem gptkb:Tor_functor gptkb:Ideal gptkb:Coordinate_ring |
| gptkbp:bfsLayer |
6
|