Theorems · Theorem · commutative algebra
Ideal.bot_isMaximal
∀ {K : Type u} [inst : DivisionSemiring K], ⊥.IsMaximal- Defined in
- Mathlib.RingTheory.Ideal.Maximal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionSemiring
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.
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- ne_of_gtproof · cited by 637
- Ideal.IsMaximalstatement · cited by 452
- DivisionSemiringstatement and proof · cited by 216
- Ideal.eq_top_iff_oneproof · cited by 56
- Ideal.eq_bot_or_topproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.bot_quotient_isMaximal_iffproof · cited by 3
- RingHom.ker_isMaximal_of_surjectiveproof · cited by 3
- PrimeSpectrum.t1Space_iff_isFieldproof · cited by 2
- Ring.isField_iff_maximal_botproof · cited by 2
- Algebra.ker_algebraMap_isMaximal_of_isIntegralproof · cited by 0