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Theorems · Theorem · commutative algebra

IsLeftRegular.mul

∀ {R : Type u_1} [inst : Semigroup R] {a b : R}, IsLeftRegular a → IsLeftRegular b → IsLeftRegular (a * b)

In a semigroup, the product of left-regular elements is left-regular.

Defined in
Mathlib.Algebra.Regular.Basic
Cited by
5 results in Mathlib
Foundations
Depth 7 from the axioms · uses propext, Quot.sound
Assumes
Semigroup
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Around this declaration

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

IsRegular.mul · cited by 1IsRegular.mulIsLeftRegular.prod · cited by 1IsLeftRegular.prodMatrix.adjugate_mul_distrib_aux · cited by 1Matrix.adjugate_mul_distr…Matrix.Nonsingular.mul · cited by 1Nonsingular.mulmul_isLeftRegular_iff · cited by 0mul_isLeftRegular_iffSemigroup · cited by 202SemigroupIsLeftRegular · cited by 97IsLeftRegularcomp_mul_left · cited by 4comp_mul_leftIsLeftRegular.mulCITED BYCITES

Cites3

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Cited by5

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