Theorems · Theorem · commutative algebra
Submodule.fg_unit
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
(I : (Submodule R A)ˣ), (↑I).FG- Defined in
- Mathlib.RingTheory.Finiteness.Subalgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Unitsstatement and proof · cited by 2,804
- le_reflproof · cited by 2,061
- Units.valstatement and proof · cited by 1,966
- mul_assocproof · cited by 1,667
Cited by3
Results whose statement or proof uses this declaration.
- FractionalIdeal.fg_unitproof · cited by 1
- Units.submodule_isFractionalproof · cited by 1
- Submodule.fg_of_isUnitproof · cited by 0