Theorems · Theorem · commutative algebra
Submodule.mul_eq_bot
∀ {R : Type u} [inst : Semiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Module R A]
[inst_3 : IsScalarTower R A A] [NoZeroDivisors A] {M N : Submodule R A}, M * N = ⊥ ↔ M = ⊥ ∨ N = ⊥- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- IsScalarTowerstatement and proof · cited by 3,896
- NoZeroDivisorsstatement and proof · cited by 545
- mul_eq_zeroproof · cited by 94
- Submodule.eq_bot_iffproof · cited by 31
- Submodule.ne_bot_iffproof · cited by 28
- Submodule.mul_mem_mulproof · cited by 27
- Submodule.mul_botproof · cited by 9
- Submodule.bot_mulproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.mul_eq_botproof · cited by 3