Matrix expression of finite Boolean-type algebras

作者：

Highlights：

• The structure matrices for most finite Boolean-type lattices and complementation algebras are presented.

• Using the structure matrices, the homomorphisms and isomorphisms of BTAs are investigated.

• The decomposition of a BTA is considered, which means decomposing a BTA into a product of two BTAs, and a straightforward verifiable necessary and sufficient condition is obtained.

摘要

•The structure matrices for most finite Boolean-type lattices and complementation algebras are presented.•Using the structure matrices, the homomorphisms and isomorphisms of BTAs are investigated.•The decomposition of a BTA is considered, which means decomposing a BTA into a product of two BTAs, and a straightforward verifiable necessary and sufficient condition is obtained.

论文关键词：Boolean-type algebra,Lattice,Complementation,Universal algebra,Semi-tensor product of matrices

论文评审过程：Received 22 September 2020, Revised 1 December 2020, Accepted 3 December 2020, Available online 19 December 2020, Version of Record 19 December 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125880