Theorems · Theorem · commutative algebra
AdicCompletion.isMaximal_map_of_le
∀ {R : Type u_1} [inst : CommRing R] (I m : Ideal R) [m.IsMaximal],
I ≤ m → I.FG → (Ideal.map (algebraMap R (AdicCompletion I R)) m).IsMaximal- Cited by
- 3 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIdeal.IsMaximal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- HasQuotient.Quotientproof · cited by 2,301
- Ideal.mapstatement and proof · cited by 692
- Ideal.Quotient.mkproof · cited by 610
- AlgHom.toRingHomproof · cited by 490
- Ideal.IsMaximalstatement and proof · cited by 452
- Ideal.comapproof · cited by 443
- AdicCompletionstatement and proof · cited by 160
- Ideal.Quotient.mk_surjectiveproof · cited by 134
Cited by3
Results whose statement or proof uses this declaration.
- AdicCompletion.isLocalRing_of_fgproof · cited by 4
- AdicCompletion.maximalIdeal_eq_map_of_fgproof · cited by 3
- AdicCompletion.maximalIdeal_eq_mapproof · cited by 2