Theorems · Theorem · group theory
not_isRegular_zero
∀ {R : Type u_1} [inst : MulZeroClass R] [Nontrivial R], ¬IsRegular 0In a non-trivial ring, the element 0 is not regular -- with typeclasses.
- Defined in
- Mathlib.Algebra.GroupWithZero.Regular
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- MulZeroClassNontrivial
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Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement and proof · cited by 2,416
- MulZeroClassstatement and proof · cited by 232
- IsRegularstatement and proof · cited by 116
- IsRegular.ne_zeroproof · cited by 7
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