  5 Kleene and Omega
Algebra
Let denote ,
is an idempotent left semiring iff (for )
 is a commutative monoid , i.e.,
 is a monoid, i.e.,



 implies where iff
is a Boolean idempotent left semiring iff
 is an idempotent left semiring
 (Huntington equation)
As usual we have the following

 (greatest element w.r.t. , i.e. )
 (smallest element w.r.t. , i.e., )
is a Boolean strong left (lazy) Kleene algebra iff
 is a Boolean idempotent left semiring

 implies
 implies
is a Boolean left (lazy) omega algebra iff
 is a Boolean strong left (lazy) Kleene algebra

 implies
  