Theorems · Theorem · commutative algebra
DirectSum.IsInternal.baseChange
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {S : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] (ℳ : ι → Submodule R M) [inst_3 : DecidableEq ι] [inst_4 : CommSemiring S]
[inst_5 : Algebra R S], DirectSum.IsInternal ℳ → DirectSum.IsInternal fun i => Submodule.baseChange S (ℳ i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement · cited by 2,545
- DirectSum.IsInternalstatement and proof · cited by 65
- Submodule.baseChangestatement and proof · cited by 36
- DirectSum.Decomposition.isInternalproof · cited by 6
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