Theorems · Theorem · commutative algebra
isRegular_one
∀ {R : Type u_1} [inst : MulOneClass R], IsRegular 1If multiplying by 1 on either side is the identity, 1 is regular.
- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- MulOneClassstatement and proof · cited by 1,018
- IsRegularstatement · cited by 116
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.Sequence.span_degreeLTproof · cited by 3
- isRightRegular_of_mul_eq_oneproof · cited by 2
- isLeftRegular_of_mul_eq_oneproof · cited by 2
- MvPolynomial.monomial_one_mul_cancel_left_iffproof · cited by 1
- MvPolynomial.monomial_one_mul_cancel_right_iffproof · cited by 1
- IsLeftRegular.prodproof · cited by 1
- IsRightRegular.prodproof · cited by 1
- MonomialOrder.Monic.prodproof · cited by 0