Theorems · Theorem · commutative algebra
Ideal.Quotient.smul_top
∀ {R : Type u_5} [inst : CommRing R] (a : R) (I : Ideal R), a • ⊤ = R ∙ Submodule.Quotient.mk a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- mul_oneproof · cited by 3,885
- HasQuotient.Quotientstatement · cited by 2,301
- Submodule.spanstatement and proof · cited by 1,504
- Ideal.Quotient.mkproof · cited by 610
- Algebra.smul_defproof · cited by 287
- Submodule.Quotient.mkstatement · cited by 184
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.exact_mulQuot_quotOfMulproof · cited by 1