Theorems · Definition · commutative algebra

HomogeneousSubmodule.noConfusionType

Sort u →
  {ιA : Type u_1} →
    {ιM : Type u_2} →
      {σA : Type u_3} →
        {σM : Type u_4} →
          {A : Type u_5} →
            {M : Type u_6} →
              [inst : Semiring A] →
                [inst_1 : AddCommMonoid M] →
                  [inst_2 : Module A M] →
                    {𝒜 : ιA → σA} →
                      {ℳ : ιM → σM} →
                        [inst_3 : DecidableEq ιA] →
                          [inst_4 : AddMonoid ιA] →
                            [inst_5 : SetLike σA A] →
                              [inst_6 : AddSubmonoidClass σA A] →
                                [inst_7 : GradedRing 𝒜] →
                                  [inst_8 : DecidableEq ιM] →
                                    [inst_9 : SetLike σM M] →
                                      [inst_10 : AddSubmonoidClass σM M] →
                                        [inst_11 : DirectSum.Decomposition ℳ] →
                                          [inst_12 : VAdd ιA ιM] →
                                            [inst_13 : SetLike.GradedSMul 𝒜 ℳ] →
                                              HomogeneousSubmodule 𝒜 ℳ →
                                                {ιA' : Type u_1} →
                                                  {ιM' : Type u_2} →
                                                    {σA' : Type u_3} →
                                                      {σM' : Type u_4} →
                                                        {A' : Type u_5} →
                                                          {M' : Type u_6} →
                                                            [inst' : Semiring A'] →
                                                              [inst'_1 : AddCommMonoid M'] →
                                                                [inst'_2 : Module A' M'] →
                                                                  {𝒜' : ιA' → σA'} →
                                                                    {ℳ' : ιM' → σM'} →
                                                                      [inst'_3 : DecidableEq ιA'] →
                                                                        [inst'_4 : AddMonoid ιA'] →
                                                                          [inst'_5 : SetLike σA' A'] →
                                                                            [inst'_6 : AddSubmonoidClass σA' A'] →
                                                                              [inst'_7 : GradedRing 𝒜'] →
                                                                                [inst'_8 : DecidableEq ιM'] →
                                                                                  [inst'_9 : SetLike σM' M'] →
                                                                                    [inst'_10 :
                                                                                        AddSubmonoidClass σM' M'] →
                                                                                      [inst'_11 :
                                                                                          DirectSum.Decomposition ℳ'] →
                                                                                        [inst'_12 : VAdd ιA' ιM'] →
                                                                                          [inst'_13 :
                                                                                              SetLike.GradedSMul 𝒜'
                                                                                                ℳ'] →
                                                                                            HomogeneousSubmodule 𝒜' ℳ' →
                                                                                              Sort u

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleDecidableEqAddMonoidSetLikeAddSubmonoidClassGradedRingDecidableEqSetLikeAddSubmonoidClassDirectSum.DecompositionVAddSetLike.GradedSMulSemiringAddCommMonoidModuleDecidableEqAddMonoidSetLikeAddSubmonoidClassGradedRingDecidableEqSetLikeAddSubmonoidClassDirectSum.DecompositionVAddSetLike.GradedSMul