Theorems · Definition · ring theory

NonUnitalSubsemiring.prod

{R : Type u} →
  {S : Type v} →
    [inst : NonUnitalNonAssocSemiring R] →
      [inst_1 : NonUnitalNonAssocSemiring S] →
        NonUnitalSubsemiring R → NonUnitalSubsemiring S → NonUnitalSubsemiring (R × S)

Given NonUnitalSubsemirings s, t of semirings R, S respectively, s.prod t is s × t as a non-unital subsemiring of R × S.

Defined in

Mathlib.RingTheory.NonUnitalSubsemiring.Basic

Cited by

9 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

NonUnitalNonAssocSemiringNonUnitalNonAssocSemiring