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Bounded zero semilattices are bounded semilattices with an absorbing element that satisfies combine(x, absorbing) == combine(absorbing, x) == absorbing.

A commutative zero group is a commutative group with an absorbing element that satisfies combine(x, absorbing) == combine(absorbing, x) == absorbing.

CommutativeZeroMonoid represents a commutative zero monoid.

A zero monoid is commutative if for all x and y, x |+| y === y |+| x.

CommutativeZeroSemigroup represents a commutative zero semigroup.

A zero semigroup is commutative if for all x and y, x |+| y === y |+| x.

Zero bands are bands with an absorbing element that satisfies combine(x, absorbing) == combine(absorbing, x) == absorbing.

A group with an absorbing element.

A monoid with an absorbing element.

A zero semigroup is a semigroup with an absorbing element. A zero semigroup is a specialization of a semigroup, so its operation must be associative. Additionally, combine(x, absorbing) == combine(absorbing, x) == absorbing. For example, if we have ZeroSemigroup[Int], with combine as integer multiplication, then absorbing == 0.

Zero semilattices are semilattices with an absorbing element that satisfies combine(x, absorbing) == combine(absorbing, x) == absorbing.