Theorems · Theorem · commutative algebra
Submodule.IsPrincipal.generator_bot
∀ {R : Type u} {M : Type v} [inst : AddCommMonoid M] [inst_1 : Semiring R] [inst_2 : Module R M],
Submodule.IsPrincipal.generator ⊥ = 0- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidSemiringModule
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Cites7
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
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- Submodule.IsPrincipal.generatorstatement · cited by 56
- Submodule.IsPrincipal.eq_bot_iff_generator_eq_zeroproof · cited by 7
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