Mathlib Map

Theorems · Definition · commutative algebra

Ideal.ofList

{R : Type u_1} → [inst : Semiring R] → List R → Ideal R

The ideal generated by a list of elements.

Defined in
Mathlib.RingTheory.Regular.RegularSequence
Cited by
33 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
Semiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ideal.ofList_nil · cited by 8Ideal.ofList_nilSubmodule.quotOfListConsSMulTopEquivQuotSMulTopInner · cited by 7Submodule.quotOfListConsS…RingTheory.Sequence.isRegular_iff · cited by 6Sequence.isRegular_iffRingTheory.Sequence.isWeaklyRegular_cons_iff · cited by 6Sequence.isWeaklyRegular_…RingTheory.Sequence.IsRegular.top_ne_smul · cited by 4IsRegular.top_ne_smulAddEquiv.isWeaklyRegular_congr · cited by 3AddEquiv.isWeaklyRegular_…Ideal.ofList_cons · cited by 3Ideal.ofList_consRingTheory.Sequence.IsRegular.casesOn · cited by 2IsRegular.casesOnRingTheory.Sequence.isRegular_cons_iff · cited by 2Sequence.isRegular_cons_i…RingTheory.Sequence.isWeaklyRegular_iff_Fin · cited by 2Sequence.isWeaklyRegular_…Ideal.map_ofList · cited by 2Ideal.map_ofListRingTheory.Sequence.IsWeaklyRegular.of_perm_of_subset_jacobson_annihilator · cited by 2IsWeaklyRegular.of_perm_o…Submodule.top_eq_ofList_cons_smul_iff · cited by 2Submodule.top_eq_ofList_c…Module.supportDim_add_length_eq_supportDim_of_isRegular · cited by 1Module.supportDim_add_len…RingTheory.Sequence.isRegular_cons_iff' · cited by 1Sequence.isRegular_cons_i…Semiring · cited by 13802SemiringSet.ofPred · cited by 6101Set.ofPredIdeal · cited by 4748IdealIdeal.span · cited by 948Ideal.spanIdeal.ofListCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by41

Results whose statement or proof uses this declaration.