Theorems · Theorem · ring theory
Subalgebra.algebraMap_mem
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (S : Subalgebra R A)
(r : R), (algebraMap R A) r ∈ S- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses no axioms
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Subalgebrastatement and proof · cited by 1,353
- algebraMap_memproof · cited by 23
Cited by29
Results whose statement or proof uses this declaration.
- Subalgebra.opproof · cited by 30
- Subalgebra.range_subsetproof · cited by 5
- Subalgebra.coe_iSup_of_directedproof · cited by 4
- MvPolynomial.adjoin_range_Xproof · cited by 4
- Algebra.surjective_algebraMap_iffproof · cited by 4
- Algebra.adjoin_adjoin_coe_preimageproof · cited by 3
- IsPrimitiveRoot.adjoin_isCyclotomicExtensionproof · cited by 3
- Algebra.adjoin_singleton_algebraMapproof · cited by 3
- ValuationSubring.le_ofPrimeproof · cited by 2
- Algebra.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRootproof · cited by 2
- GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous_ne_zeroproof · cited by 2