Statements (97)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
algebraic structures
|
| gptkbp:developedBy |
gptkb:David_Hilbert
gptkb:Emil_Artin gptkb:Emmy_Noether gptkb:Ernst_Steinitz gptkb:Nathan_Jacobson gptkb:Richard_Dedekind gptkb:Bartel_van_der_Waerden gptkb:Joseph_Wedderburn gptkb:Issai_Schur |
| gptkbp:hasApplication |
gptkb:algebraic_geometry
gptkb:topology coding theory cryptography functional analysis number theory physics combinatorics |
| gptkbp:hasConcept |
gptkb:Hilbert's_basis_theorem
gptkb:Noetherian_module gptkb:Artin–Wedderburn_theorem gptkb:Artinian_module gptkb:Chinese_remainder_theorem gptkb:Krull_dimension gptkb:Wedderburn's_theorem gptkb:Morita_equivalence gptkb:Zorn's_lemma gptkb:module_automorphism gptkb:module_endomorphism gptkb:module_homomorphism gptkb:semisimple_module gptkb:structure_theorem_for_modules_over_a_PID automorphism annihilator finitely generated module flat module injective module localization maximal ideal projective module spectrum of a ring tensor product ascending chain condition descending chain condition direct product direct sum endomorphism isomorphism free module simple module prime ideal quotient ring subring chain conditions extension of rings minimal ideal module annihilator module direct product module direct sum module extension module isomorphism module quotient module submodule module tensor product |
| https://www.w3.org/2000/01/rdf-schema#label |
Ring theory
|
| gptkbp:includes |
gptkb:Noetherian_rings
gptkb:Artinian_rings gptkb:Jacobson_radical fields commutative rings ideals modules units integral domains local rings polynomial rings semisimple rings center of a ring ring homomorphisms noncommutative rings group rings division rings matrix rings nilpotent elements polynomial identities principal ideal domains representation theory of rings simple rings unique factorization domains zero divisors |
| gptkbp:relatedTo |
abstract algebra
|
| gptkbp:studies |
rings
|
| gptkbp:bfsParent |
gptkb:Homomorphism
gptkb:Isomorphism gptkb:Ideal |
| gptkbp:bfsLayer |
6
|