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Theorems · Theorem · group theory

smul_eq_zero_of_right

∀ {M : Type u_1} {A : Type u_7} [inst : Zero A] [inst_1 : SMulZeroClass M A] (a : M) {b : A}, b = 0 → a • b = 0
Defined in
Mathlib.Algebra.GroupWithZero.Action.Defs
Cited by
5 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
ZeroSMulZeroClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

right_ne_zero_of_smul · cited by 6right_ne_zero_of_smulAffine.Simplex.midpoint_faceOppositeCentroid_eulerPoint · cited by 1Simplex.midpoint_faceOppo…Module.associatedPrimes.comap_mem_associatedPrimes_of_mem_associatedPrimes_of_isLocalizedModule_of_fg · cited by 1associatedPrimes.comap_me…fwdDiff_iter_sum_mul_pow_eq_zero · cited by 0fwdDiff_iter_sum_mul_pow_…LinearMap.BilinForm.IsRefl.smul · cited by 0IsRefl.smulsmul_zero · cited by 665smul_zeroSMulZeroClass · cited by 213SMulZeroClasssmul_eq_zero_of_rightCITED BYCITES

Cites2

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Cited by5

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