Statements (118)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:academic
gptkb:mathematical_concept |
| gptkbp:hasConcept |
gptkb:Dedekind_domain
gptkb:Functor gptkb:Hilbert's_Nullstellensatz gptkb:Zariski_topology gptkb:conductor gptkb:Noetherian_ring gptkb:local_ring gptkb:spectrum_of_a_ring gptkb:Artin–Rees_lemma gptkb:Artinian_ring gptkb:Auslander–Buchsbaum_formula gptkb:Betti_number gptkb:Chinese_remainder_theorem gptkb:Cohen–Macaulay_ring gptkb:Frobenius_endomorphism gptkb:Frobenius_splitting gptkb:Gorenstein_ring gptkb:Grothendieck_group gptkb:Hilbert_basis_theorem gptkb:Hilbert_function gptkb:Hilbert_polynomial gptkb:Koszul_complex gptkb:Krull's_principal_ideal_theorem gptkb:Krull–Schmidt_theorem gptkb:Krull_dimension gptkb:Krull_ring gptkb:Matlis_duality gptkb:Nakayama's_lemma gptkb:valuation_ring gptkb:Gauss's_lemma gptkb:Jacobson_radical gptkb:regular_ring gptkb:Grothendieck's_existence_theorem gptkb:Nagata_ring gptkb:prime_ideal gptkb:module_homomorphism gptkb:Eisenstein's_criterion gptkb:exact_sequence gptkb:integral_domain gptkb:principal_ideal_domain gptkb:unique_factorization_domain polynomial ring Fitting ideal Rees algebra annihilator associated prime canonical module completion depth depth lemma depth of a module depth of a ring dimension theory divisor finitely generated module flat module homological dimension injective module integral closure integral extension local cohomology localization maximal ideal minimal prime power series ring primary decomposition primary ideal projective module regular local ring regular sequence support of a module syzygy syzygy module tensor product tight closure valuation multiplicity discrete valuation ring graded ring projective dimension ring homomorphism adjoint functor universal property Bass numbers Spec of a ring blowup algebra fraction field normal ring chain condition reduced ring minimal resolution category of modules Dedekind–Mertens lemma Japanese ring Prüfer domain Serre's criterion excellent ring filtered ring flat dimension henselian ring injective dimension injective hull nilradical seminormal ring total quotient ring valuation domain |
| gptkbp:relatedTo |
gptkb:algebraic_geometry
algebraic number theory homological algebra |
| gptkbp:studies |
algebraic structures
commutative rings ideals modules |
| gptkbp:bfsParent |
gptkb:Graduate_Studies_in_Mathematics
|
| gptkbp:bfsLayer |
7
|
| https://www.w3.org/2000/01/rdf-schema#label |
Commutative Algebra
|