Theorems · Theorem · number theory
AddChar.to_mulShift_inj_of_isPrimitive
∀ {R : Type u} [inst : CommRing R] {R' : Type v} [inst_1 : CommMonoid R'] {ψ : AddChar R R'},
ψ.IsPrimitive → Function.Injective ψ.mulShiftThe map associating to a : R the multiplicative shift of ψ by a
is injective when ψ is primitive.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingCommMonoid
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- CommMonoidstatement and proof · cited by 2,264
- AddCharstatement and proof · cited by 286
- add_neg_cancelproof · cited by 213
- AddChar.mulShiftstatement and proof · cited by 26
- AddChar.IsPrimitivestatement and proof · cited by 22
- AddChar.mulShift_mulproof · cited by 2
- AddChar.mulShift_zeroproof · cited by 2
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