Theorems · Theorem · ring theory

MonoidAlgebra.isGroupLikeElem_iff_mem_range_single_one

∀ {R : Type u_1} {M : Type u_8} [inst : CommRing R] [IsDomain R] {x : MonoidAlgebra R M},
  IsGroupLikeElem R x ↔ x ∈ Set.range fun x => MonoidAlgebra.single x 1

Defined in: Mathlib.RingTheory.Bialgebra.MonoidAlgebra
Cited by: 1 results in Mathlib
Foundations: Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain

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Cites27

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setstatement · cited by 53,352
CommRingstatement and proof · cited by 17,173
Set.rangestatement and proof · cited by 4,705
mul_oneproof · cited by 3,885
IsDomainstatement and proof · cited by 2,196
Submodule.spanproof · cited by 1,504
Finsupp.supportproof · cited by 828
MonoidAlgebrastatement and proof · cited by 590
Set.image_congrproof · cited by 533
Finsupp.sumproof · cited by 481
smul_eq_mulproof · cited by 357

Cited by1

Results whose statement or proof uses this declaration.

MonoidAlgebra.isGroupLikeElem_iff_mem_range_ofproof · cited by 0