Theorems · Theorem · commutative algebra

Subsemiring.isMulCommutative_iSup

∀ {R : Type u} [inst : NonAssocSemiring R] {ι : Sort u_1} [Nonempty ι] {S : ι → Subsemiring R}
  [hS : ∀ (i : ι), IsMulCommutative ↥(S i)], Directed (fun x1 x2 => x1 ≤ x2) S → IsMulCommutative ↥(⨆ i, S i)

Defined in

Mathlib.Algebra.Ring.Subsemiring.Basic

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonAssocSemiringNonemptyIsMulCommutative