Theorems · Theorem · commutative algebra
DividedPowerAlgebra.dp_zero
∀ {R : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {m : M},
DividedPowerAlgebra.dp R 0 m = 1- Cited by
- 6 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- MvPolynomial.Xproof · cited by 552
- RingCon.Quotientproof · cited by 118
- RingCon.toQuotientproof · cited by 69
- DividedPowerAlgebra.ringConstatement and proof · cited by 49
- DividedPowerAlgebrastatement and proof · cited by 48
- DividedPowerAlgebra.dpstatement · cited by 31
- RingCon.le_ringConGenproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- DividedPowerAlgebra.dp_nullproof · cited by 2
- DividedPowerAlgebra.dp_sumproof · cited by 1
- DividedPowerAlgebra.prod_dpproof · cited by 1
- DividedPowerAlgebra.LinearMap.dp_zeroproof · cited by 0
- DividedPowerAlgebra.natFactorial_mul_dp_eqproof · cited by 0
- DividedPowerAlgebra.submodule_span_prod_dp_eq_topproof · cited by 0