Theorems · Inductive type · functional analysis
PreQuasiregular
Type u_1 → Type u_1
A type synonym for non-unital rings where an alternative monoid structure is introduced.
If R is a non-unital semiring, then PreQuasiregular R is equipped with the monoid structure
with binary operation fun x y ↦ y + x + x * y and identity 0. Elements of R which are
invertible in this monoid satisfy the predicate IsQuasiregular.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by30
Results whose statement or proof uses this declaration.
- IsQuasiregularproof · cited by 18
- PreQuasiregular.equivstatement · cited by 11
- PreQuasiregular.valstatement and proof · cited by 6
- Unitization.unitsFstOne_mulEquiv_quasiregularstatement and proof · cited by 5
- isQuasiregular_iffproof · cited by 4
- PreQuasiregular.mk.injstatement · cited by 1
- PreQuasiregular.mk.noConfusionstatement · cited by 1
- PreQuasiregular.add_inv_add_mul_eq_zerostatement and proof · cited by 1
- PreQuasiregular.equiv_symm_applystatement and proof · cited by 1
- PreQuasiregular.inv_add_add_mul_eq_zerostatement and proof · cited by 1
- Unitization.val_unitsFstOne_mulEquiv_quasiregular_applystatement · cited by 1
- PreQuasiregular.toPistatement and proof · cited by 1