Polynomial ring in finitely many variables over a field

URI: https://gptkb.org/entity/Polynomial_ring_in_finitely_many_variables_over_a_field
GPTKB entity
Statements (33)
Predicate Object
gptkbp:instanceOf gptkb:algebra
Noetherian ring
commutative ring
integral domain
unique factorization domain
gptkbp:has_base_field gptkb:Field
gptkbp:has_Krull_dimension number of variables
gptkbp:has_variables finite set
https://www.w3.org/2000/01/rdf-schema#label Polynomial ring in finitely many variables over a field
gptkbp:is_a_domain yes
gptkbp:is_a_finitely_generated_k-algebra yes
gptkbp:is_a_finitely_generated_module_over_itself yes
gptkbp:is_a_finitely_generated_module_over_the_base_field no
gptkbp:is_a_finitely_presented_algebra yes
gptkbp:is_a_free_module_over_field yes
gptkbp:is_a_Hopf_algebra yes
gptkbp:is_a_Jacobson_ring yes
gptkbp:is_a_local_ring no
gptkbp:is_a_principal_ideal_domain no
gptkbp:is_a_reduced_ring yes
gptkbp:is_a_regular_ring yes
gptkbp:is_a_simple_ring no
gptkbp:is_a_universal_enveloping_algebra no
gptkbp:is_denoted k[x_1, ..., x_n]
gptkbp:is_finitely_generated_as_algebra_over_field yes
gptkbp:is_graded yes
gptkbp:is_not_a_field yes
gptkbp:satisfies_Hilbert's_basis_theorem yes
gptkbp:used_in gptkb:algebraic_geometry
gptkb:commutative_algebra
invariant theory
gptkbp:bfsParent gptkb:Noetherian_ring_(in_the_commutative_case)
gptkbp:bfsLayer 7