Mathlib Map

Structures · Algebra

CommGroupWithZero

A type G₀ is a commutative “group with zero” if it is a commutative monoid with zero element (distinct from 1) such that every nonzero element is invertible. The type is required to come with an “inverse” function, and the inverse of 0 must be 0.

Defined in
Mathlib.Algebra.GroupWithZero.Defs
Shape
One type argument · adds div_eq_mul_inv, zpow_zero', zpow_succ', zpow_neg', inv_zero, mul_inv_cancel

Extends2

Extended by2

Forgetful instances

Every CommGroupWithZero is also a

Concrete types that are instances11

  • Rat
  • DirectLimit
  • OreLocalization
  • SignType
  • ValuationRing.ValueGroup
  • MonoidWithZeroHom.ValueGroup₀
  • Subtype
  • OrderDual
  • ULift
  • Lex
  • WithZero

How is a type an instance?

Loading the hierarchy index…

Assumed by138

Ancestors38