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Theorems · Theorem · ring theory

Subalgebra.op_le_op_iff

∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
  {S₁ S₂ : Subalgebra R A}, S₁.op ≤ S₂.op ↔ S₁ ≤ S₂
Defined in
Mathlib.Algebra.Algebra.Subalgebra.MulOpposite
Cited by
0 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebra
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Around this declaration

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Subalgebra.opEquiv · cited by 18Subalgebra.opEquivSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringSubalgebra · cited by 1353SubalgebraMulOpposite · cited by 1135MulOppositeFunction.Surjective.forall · cited by 214Surjective.forallSubalgebra.op · cited by 30Subalgebra.opMulOpposite.op_surjective · cited by 21MulOpposite.op_surjectiveSubalgebra.op_le_op_iffCITED BYCITES

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Cited by1

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