Theorems · Definition · ring theory

StarSubalgebra.ofClass

{S : Type u_6} →
  {R : Type u_7} →
    {A : Type u_8} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Algebra R A] →
            [inst_3 : StarRing R] →
              [inst_4 : StarRing A] →
                [inst_5 : StarModule R A] →
                  [inst_6 : SetLike S A] →
                    [SubsemiringClass S A] → [SMulMemClass S R A] → [StarMemClass S A] → S → StarSubalgebra R A

The actual StarSubalgebra obtained from an element of a type satisfying SubsemiringClass, SMulMemClass and StarMemClass.

Defined in

Mathlib.Algebra.Star.Subalgebra

Cited by

2 results in Mathlib

Foundations

Depth 21 from the axioms · uses no axioms

Assumes

CommSemiringSemiringAlgebraStarRingStarRingStarModuleSetLikeSubsemiringClassSMulMemClassStarMemClass