Matrix expression of finite Boolean-type algebras

Abstract

This paper provides a systematic matrix description for finite Boolean- type algebras (BTAs). 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 of BTA) are presented. Via their matrix expression, the construction and certain properties of BTAs are investigated, including the homomorphism and isomorphism, as well as the decomposition. Moreover, straightforward verifiable conditions are obtained to detect the properties above by means of logical matrices operations.