Theorems · Theorem · commutative algebra
IsSMulRegular.of_flat
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S]
[Module.Flat R S] {x : R}, IsSMulRegular R x → IsSMulRegular S ((algebraMap R S) x)- Defined in
- Mathlib.RingTheory.Flat.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 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.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Module.Flatstatement and proof · cited by 279
- IsSMulRegularstatement and proof · cited by 128
- IsBaseChange.linearMapproof · cited by 4
- IsSMulRegular.of_flat_of_isBaseChangeproof · cited by 3
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