Theorems · Theorem · commutative algebra
FractionalIdeal.coeIdeal_sup
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
(I J : Ideal R), ↑(I ⊔ J) = ↑I + ↑J- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Idealstatement and proof · cited by 4,748
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement · cited by 423
- FractionalIdeal.coeIdealstatement and proof · cited by 109
- FractionalIdeal.coeToSubmodule_injectiveproof · cited by 19
- IsLocalization.coeSubmodule_supproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- FractionalIdeal.coeIdealHomproof · cited by 3
- FractionalIdeal.sup_mul_infproof · cited by 0