A Boolean algebra is a Boolean lattice such that and are considered as operators (unary and nullary respectively) on the algebraic system. In other words, a morphism (or a Boolean algebra homomorphism) between two Boolean algebras must preserve and . As a result, the category of Boolean algebras and the category of Boolean lattices are not the same (and the former is a subcategory of the latter).
any Boolean ring has characteristic , for ,
and hence a commutative ring, for , so , and therefore .
To view a Boolean lattice as a Boolean ring, define
The category of Boolean algebras is naturally equivalent to the category of Boolean rings.
- 1 G. Grätzer, General Lattice Theory, 2nd Edition, Birkhäuser (1998).
- 2 R. Sikorski, Boolean Algebras, 2nd Edition, Springer-Verlag, New York (1964).
|Date of creation||2013-03-22 12:27:20|
|Last modified on||2013-03-22 12:27:20|
|Last modified by||mathcam (2727)|