Polynomial ring in finitely many variables over a field

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:algebra gptkb:Noetherian_ring gptkb:commutative_ring gptkb:integral_domain gptkb:unique_factorization_domain
gptkbp:has_base_field	gptkb:Field
gptkbp:has_Krull_dimension	number of variables
gptkbp:has_variables	finite set
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
https://www.w3.org/2000/01/rdf-schema#label	Polynomial ring in finitely many variables over a field