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Theorems · Theorem · group theory

CommSemigroup.mul_comm

∀ {G : Type u} [self : CommSemigroup G] (a b : G), a * b = b * a

Multiplication is commutative in a commutative multiplicative magma.

Defined in
Mathlib.Algebra.Group.Defs
Cited by
0 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CommSemigroup
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Function.Injective.commMonoid · cited by 0Injective.commMonoidFunction.Injective.commSemiring · cited by 0Injective.commSemiringFunction.Injective.nonUnitalCommSemiring · cited by 0Injective.nonUnitalCommSe…Function.Surjective.nonUnitalCommSemiring · cited by 0Surjective.nonUnitalCommS…Function.Surjective.commMonoid · cited by 0Surjective.commMonoidFunction.Injective.divisionCommMonoid · cited by 0Injective.divisionCommMon…Function.Surjective.commSemiring · cited by 0Surjective.commSemiringCommSemigroup · cited by 62CommSemigroupCommSemigroup.mul_commCITED BYCITES

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