Theorems · Theorem · ring theory
algebraMap_mem
∀ {S : Type u_1} {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : SetLike S A] [OneMemClass S A] [SMulMemClass S R A] (s : S) (r : R), (algebraMap R A) r ∈ s- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- SetLikestatement and proof · cited by 1,084
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
- OneMemClass.one_memproof · cited by 87
- SMulMemClassstatement and proof · cited by 77
- SMulMemClass.smul_memproof · cited by 55
- OneMemClassstatement and proof · cited by 21
Cited by23
Results whose statement or proof uses this declaration.
- Subalgebra.algebraMap_memproof · cited by 28
- Algebra.adjoin_inductionstatement and proof · cited by 22
- StarAlgebra.adjoin_inductionstatement and proof · cited by 2
- LocalSubring.exists_valuationRing_of_isMaxproof · cited by 2
- LocalSubring.mem_of_isMax_of_isIntegralproof · cited by 1
- Algebra.Subalgebra.restrictScalars_adjoinproof · cited by 1
- Unitization.starLift_range_leproof · cited by 1
- Algebra.sSup_toSubsemiringproof · cited by 1
- Unitization.lift_range_leproof · cited by 1
- solvableByRad.inductionstatement and proof · cited by 1
- Subring.integralClosure_le_iffproof · cited by 1
- StarSubalgebra.coe_iSup_of_directedproof · cited by 1