Theorems · Theorem · commutative algebra
Module.Flat.iff_characterModule_baer
∀ {R : Type u} {M : Type v} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M],
Module.Flat R M ↔ Module.Baer R (CharacterModule M)CharacterModule M is Baer iff M is flat.
- Defined in
- Mathlib.RingTheory.Flat.Tensor
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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Cites13
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- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearEquiv.symmproof · cited by 1,461
- Module.Flatstatement · cited by 279
- CharacterModulestatement and proof · cited by 26
- Module.Baerstatement and proof · cited by 20
- ULift.moduleEquivproof · cited by 18
- Module.Baer.iff_injectiveproof · cited by 4
- Module.Flat.equiv_iffproof · cited by 2
- Module.Baer.congrproof · cited by 1
- Module.Flat.iff_characterModule_injectiveproof · cited by 1
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