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Theorems · Theorem · number theory

MulChar.IsQuadratic.sq_eq_one

∀ {R : Type u_1} [inst : CommMonoid R] {R' : Type u_2} [inst_1 : CommRing R'] {χ : MulChar R R'},
  χ.IsQuadratic → χ ^ 2 = 1

The square of a quadratic character is the trivial character.

Defined in
Mathlib.NumberTheory.MulChar.Basic
Cited by
2 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidCommRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MulChar.IsQuadratic.pow_even · cited by 1IsQuadratic.pow_evenMulChar.IsQuadratic.gaussSum_frob · cited by 1IsQuadratic.gaussSum_frobCommRing · cited by 17173CommRingCommMonoid · cited by 2264CommMonoidMulChar · cited by 186MulCharpow_two · cited by 150pow_twoinv_mul_cancel · cited by 107inv_mul_cancelMulChar.IsQuadratic · cited by 18MulChar.IsQuadraticMulChar.IsQuadratic.inv · cited by 2IsQuadratic.invIsQuadratic.sq_eq_oneCITED BYCITES

Cites7

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Cited by2

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