On Monadic Operators on Modal Pseudocomplemented De Morgan Algebras and Tetravalent Modal Algebras

摘要

In our paper, monadic modal pseudocomplemented De Morgan algebras (or mmpM) are considered following Halmos' studies on monadic Boolean algebras. Hence, their topological representation theory (Halmos-Priestley's duality) is used successfully. Lattice congruences of an mmpM is characterized and the variety of mmpMs is proven semisimple via topological representation. Furthermore and among other things, the poset of principal congruences is investigated and proven to be a Boolean algebra; therefore, every principal congruence is a Boolean congruence. All these conclusions contrast sharply with known results for monadic De Morgan algebras. Finally, we show that the above results for mmpM are verified for monadic tetravalent modal algebras.