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Theorems · Theorem · commutative algebra

isRegular_iff

∀ {R : Type u_1} [inst : Mul R] {c : R}, IsRegular c ↔ IsLeftRegular c ∧ IsRightRegular c
Defined in
Mathlib.Algebra.Regular.Defs
Cited by
6 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
Mul
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Around this declaration

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

IsArtinianRing.isUnit_iff_isRegular_of_mulOpposite · cited by 2IsArtinianRing.isUnit_iff…IsArtinianRing.isUnit_iff_isRegular · cited by 2IsArtinianRing.isUnit_iff…isRegular_iff_eq_zero_of_mul · cited by 1isRegular_iff_eq_zero_of_…isCancelMulZero_iff_forall_isRegular · cited by 1isCancelMulZero_iff_foral…isCancelMul_iff_forall_isRegular · cited by 1isCancelMul_iff_forall_is…isRegular_star_iff · cited by 0isRegular_star_iffIsRegular · cited by 116IsRegularIsLeftRegular · cited by 97IsLeftRegularIsRightRegular · cited by 93IsRightRegularisRegular_iffCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.