Mathlib Map

Theorems · Definition · ring theory

MulSemiringAction.toRingEquiv

(G : Type u_1) → [inst : Group G] → (R : Type u_2) → [inst_1 : Semiring R] → [MulSemiringAction G R] → G →* R ≃+* R

Each element of the group defines a semiring isomorphism.

Defined in
Mathlib.Algebra.Ring.Action.Group
Cited by
13 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupSemiringMulSemiringAction

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Unitary.conjStarAlgAut · cited by 26Unitary.conjStarAlgAutMulSemiringAction.toAlgEquiv · cited by 11MulSemiringAction.toAlgEq…MulSemiringAction.toRingAut · cited by 8MulSemiringAction.toRingA…Ideal.pointwise_smul_eq_comap · cited by 5Ideal.pointwise_smul_eq_c…IsFractionRing.mulSemiringAction · cited by 4IsFractionRing.mulSemirin…MulSemiringAction.toRingAut_apply · cited by 4MulSemiringAction.toRingA…MulSemiringAction.toRingEquiv_apply_symm_apply · cited by 4MulSemiringAction.toRingE…IsArithFrobAt.conj · cited by 1IsArithFrobAt.conjMulSemiringAction.toRingEquiv_apply_apply · cited by 1MulSemiringAction.toRingE…IsArithFrobAt.mem_stabilizer · cited by 1IsArithFrobAt.mem_stabili…Unitary.toRingEquiv_conjStarAlgAut · cited by 0Unitary.toRingEquiv_conjS…Algebra.IsInvariant.exists_smul_of_under_eq_of_profinite · cited by 0IsInvariant.exists_smul_o…Ideal.smul_under · cited by 0Ideal.smul_underMulSemiringAction.toAlgEquiv_toEquiv · cited by 0MulSemiringAction.toAlgEq…MulSemiringAction.toRingEquiv_algEquiv · cited by 0MulSemiringAction.toRingE…Semiring · cited by 13802SemiringRingHom · cited by 10189RingHomGroup · cited by 6238GroupMonoidHom · cited by 3629MonoidHomRingEquiv · cited by 1147RingEquivAddEquiv · cited by 1087AddEquivMulSemiringAction · cited by 423MulSemiringActionAddEquiv.toEquiv · cited by 174AddEquiv.toEquivMulSemiringAction.toRingHom · cited by 23MulSemiringAction.toRingH…DistribMulAction.toAddEquiv · cited by 3DistribMulAction.toAddEqu…MulSemiringAction.toRingEquivCITED BYCITES

Cites10

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

Cited by17

Results whose statement or proof uses this declaration.