Theorems · Theorem · group theory
AddMonoid.exponent_prod
∀ {M₁ : Type u_1} {M₂ : Type u_2} [inst : AddMonoid M₁] [inst_1 : AddMonoid M₂],
AddMonoid.exponent (M₁ × M₂) = lcm (AddMonoid.exponent M₁) (AddMonoid.exponent M₂)The exponent of product of two additive monoids is the
lcm of the exponents of the individual additive monoids.
- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- GCDMonoid.lcmstatement and proof · cited by 78
- AddMonoid.exponentstatement and proof · cited by 70
- dvd_transproof · cited by 50
- dvd_antisymmproof · cited by 23
- Prod.snd_surjectiveproof · cited by 22
- Prod.fst_surjectiveproof · cited by 22
- dvd_lcm_leftproof · cited by 17
- dvd_lcm_rightproof · cited by 17
- addOrderOf_dvd_iff_nsmul_eq_zeroproof · cited by 17
- lcm_dvdproof · cited by 14
- AddMonoid.addOrder_dvd_exponentproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- coprime_card_of_isAddCyclic_prodproof · cited by 2