Theorems · Theorem · commutative algebra
Submodule.mker_spanSingleton
∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Algebra R A] [FaithfulSMul R A],
MonoidHom.mker (Submodule.spanSingleton R) = Submonoid.map (algebraMap R A) (IsUnit.submonoid R)- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- Submodulestatement · cited by 7,192
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement · cited by 3,086
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- MonoidWithZeroHomstatement · cited by 704
- FaithfulSMulstatement and proof · cited by 340
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