Theorems · Theorem · commutative algebra
Submodule.FG.smul
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {I : Ideal R}
[I.IsTwoSided] {N : Submodule R M}, I.FG → N.FG → (I • N).FG- Defined in
- Mathlib.RingTheory.Finiteness.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Submodule.spanproof · cited by 1,504
- Ideal.spanproof · cited by 948
- Submodule.FGstatement and proof · cited by 230
- Ideal.IsTwoSidedstatement and proof · cited by 179
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.FG.mulproof · cited by 1
- IsSemiprimaryRing.isNoetherian_iff_finite_of_jacobson_fgproof · cited by 1