Theorems · Theorem · ring theory

NonUnitalStarSubalgebra.isMulCommutative_iSup

∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : StarRing A]
  [inst_3 : Module R A] {ι : Type u_1} [inst_4 : StarRing R] [inst_5 : IsScalarTower R A A]
  [inst_6 : SMulCommClass R A A] [inst_7 : StarModule R A] [Nonempty ι] {S : ι → NonUnitalStarSubalgebra R A}
  [hS : ∀ (i : ι), IsMulCommutative ↥(S i)], Directed (fun x1 x2 => x1 ≤ x2) S → IsMulCommutative ↥(⨆ i, S i)

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalSemiringStarRingModuleStarRingIsScalarTowerSMulCommClassStarModuleNonemptyIsMulCommutative