Theorems · Theorem · commutative algebra
Algebra.isIntegral_denominator_smul
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : IsPrincipalIdealRing R] [inst_2 : CommRing S]
[inst_3 : Algebra R S] (x : S), IsIntegral R (Algebra.denominator R x • x)- Defined in
- Mathlib.RingTheory.Algebraic.Denominator
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- IsIntegralstatement · cited by 427
- IsPrincipalIdealRingstatement and proof · cited by 131
- dvd_rflproof · cited by 80
- Algebra.denominatorstatement · cited by 5
- Algebra.denominator_dvd_iffproof · cited by 3
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