Theorems · Theorem · commutative algebra
Submodule.smul_one_eq_span
∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Algebra R A] (x : A), x • 1 = R ∙ x- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- mul_oneproof · cited by 3,885
- Submodule.spanstatement and proof · cited by 1,504
- smul_eq_mulproof · cited by 357
- Submodule.pointwiseDistribMulActionstatement · cited by 105
- Submodule.one_eq_spanproof · cited by 15
- Set.smul_set_singletonproof · cited by 5
- Submodule.smul_spanproof · cited by 5
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