Theorems · Theorem · commutative algebra
Ideal.mul_top
∀ {R : Type u} [inst : Semiring R] (I : Ideal R) [I.IsTwoSided], I * ⊤ = I- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- mul_oneproof · cited by 3,885
- le_antisymmproof · cited by 2,068
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.mul_mem_rightproof · cited by 71
- Submodule.mem_topproof · cited by 58
- Ideal.mul_mem_mulproof · cited by 29
- Ideal.mul_leproof · cited by 11
Cited by42
Results whose statement or proof uses this declaration.
- Ideal.smul_top_eq_mapproof · cited by 15
- PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_modproof · cited by 10
- Ideal.isUnit_iffproof · cited by 7
- Ideal.hasBasis_nhds_zero_adicproof · cited by 6
- Ideal.isPrimary_iffproof · cited by 4
- AdicCompletion.evalₐ_liftRingHomproof · cited by 4
- Ideal.ramificationIdx'_eq_ramificationIdx'proof · cited by 3
- Perfection.teichmullerFun_sModEqproof · cited by 3
- Perfection.teichmullerFun_spec'proof · cited by 3
- Ideal.IsDedekindDomain.ramificationIdx'_eq_one_iffproof · cited by 3
- IsDedekindDomain.exists_sup_span_eqproof · cited by 2
- ClassGroup.mk_eq_one_of_coe_idealproof · cited by 2