Theorems · Theorem · ring theory
MonoidAlgebra.isGroupLikeElem_iff_mem_range_of
∀ {R : Type u_1} {M : Type u_8} [inst : CommRing R] [IsDomain R] [inst_2 : MulOneClass M] {x : MonoidAlgebra R M},
IsGroupLikeElem R x ↔ x ∈ Set.range ⇑(MonoidAlgebra.of R M)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDomainMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Set.rangestatement · cited by 4,705
- MonoidHomstatement · cited by 3,629
- IsDomainstatement and proof · cited by 2,196
- MulOneClassstatement and proof · cited by 1,018
- MonoidAlgebrastatement and proof · cited by 590
- IsGroupLikeElemstatement · cited by 39
- MonoidAlgebra.ofstatement · cited by 30
- MonoidAlgebra.isGroupLikeElem_iff_mem_range_single_oneproof · cited by 1
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