Theorems · Theorem · ring theory
AlgHom.equalizer_toSubmodule
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : Semiring B] [inst_4 : Algebra R B] {φ ψ : A →ₐ[R] B},
Subalgebra.toSubmodule (φ.equalizer ψ) = (LinearMapClass.linearMap φ).eqLocus (LinearMapClass.linearMap ψ)- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
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Cites13
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- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement · cited by 7,192
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement · cited by 1,353
- OrderEmbeddingstatement · cited by 619
- Subalgebra.toSubmodulestatement · cited by 141
- LinearMap.eqLocusstatement · cited by 22
- AlgHom.equalizerstatement · cited by 21
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