Theorems · Theorem · ring theory
MonoidAlgebra.supported_eq_span_single
∀ (R : Type u_1) {M : Type u_3} [inst : Semiring R] (s : Set M),
MonoidAlgebra.supported R R s = Submodule.span R ((fun m => MonoidAlgebra.single m 1) '' s)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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Cites20
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
- Submodulestatement · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
- Finsuppproof · cited by 5,255
- Submodule.spanstatement and proof · cited by 1,504
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
- Finsupp.singleproof · cited by 943
- MonoidAlgebrastatement · cited by 590
- Set.image_congrproof · cited by 533
- MonoidAlgebra.singlestatement and proof · cited by 253
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