Theorems · Theorem · commutative algebra
Ideal.bot_lt_of_maximal
∀ {R : Type u_5} [inst : CommSemiring R] [Nontrivial R] (M : Ideal R) [hm : M.IsMaximal], ¬IsField R → ⊥ < M- Defined in
- Mathlib.RingTheory.Ideal.Basic
- Cited by
- 3 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.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Bot.botstatement · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- Ideal.IsMaximalstatement and proof · cited by 452
- Ne.bot_ltproof · cited by 116
- IsFieldstatement and proof · cited by 103
- Ring.ne_bot_of_isMaximal_of_not_isFieldproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- FractionalIdeal.not_inv_le_one_of_ne_botproof · cited by 2
- Polynomial.isMaximal_comap_C_of_isMaximalproof · cited by 0
- IsPrincipalIdealRing.height_eq_one_of_isMaximalproof · cited by 0