Theorems · Theorem · commutative algebra
Ideal.bot_quotient_isMaximal_iff
∀ {R : Type u} [inst : Ring R] (I : Ideal R) [inst_1 : I.IsTwoSided], ⊥.IsMaximal ↔ I.IsMaximal- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- HasQuotient.Quotientstatement and proof · cited by 2,301
- DivisionRingproof · cited by 1,062
- Ideal.Quotient.mkproof · cited by 610
- Ideal.IsMaximalstatement and proof · cited by 452
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.Quotient.mk_surjectiveproof · cited by 134
- Ideal.mk_kerproof · cited by 59
- Ideal.comap_isMaximal_of_surjectiveproof · cited by 8
- Ideal.bot_isMaximalproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.jacobson_bot_of_integral_localizationproof · cited by 0
- Polynomial.isMaximal_comap_C_of_isJacobsonRingproof · cited by 0
- Polynomial.isMaximal_comap_C_of_isMaximalproof · cited by 0