Theorems · Theorem · commutative algebra
Ideal.squarefree_span_singleton
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [IsPrincipalIdealRing R] {a : R},
Squarefree (Ideal.span {a}) ↔ Squarefree a- Cited by
- 0 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- IsDomainstatement and proof · cited by 2,196
- Ideal.spanstatement and proof · cited by 948
- IsPrincipalIdealRingstatement and proof · cited by 131
- Squarefreestatement and proof · cited by 112
- Submodule.IsPrincipal.generatorproof · cited by 56
- Ideal.eq_top_of_isUnit_memproof · cited by 26
- Ideal.span_singleton_generatorproof · cited by 17
- Ideal.span_singleton_mul_span_singletonproof · cited by 12
- Submodule.IsPrincipal.generator_memproof · cited by 9
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