  Boolean-type algebra (BTA) is investigated. A BTA is decomposed into
Boolean-type lattice (BTL) and a complementation algebra (CA). When the object
set is finite, the matrix expressions of BTL and CA (and then BTA) are
presented. The construction and certain properties of BTAs are investigated via
their matrix expression, including the homomorphism and isomorphism, etc. Then
the product/decomposition of BTLs are considered. A necessary and sufficient
condition for decomposition of BTA is obtained. Finally, a universal generator
is provided for arbitrary finite universal algebras.
