Theorems · Definition · linear algebra

Module.Basis.prod

{ι : Type u_1} →
  {ι' : Type u_2} →
    {R : Type u_3} →
      {M : Type u_5} →
        {M' : Type u_6} →
          [inst : Semiring R] →
            [inst_1 : AddCommMonoid M] →
              [inst_2 : Module R M] →
                [inst_3 : AddCommMonoid M'] →
                  [inst_4 : Module R M'] → Module.Basis ι R M → Module.Basis ι' R M' → Module.Basis (ι ⊕ ι') R (M × M')

Basis.prod maps an ι-indexed basis for M and an ι'-indexed basis for M' to an ι ⊕ ι'-index basis for M × M'. For the specific case of R × R, see also Basis.finTwoProd.

Defined in

Mathlib.LinearAlgebra.Basis.Prod

Cited by

26 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModule