Ockham Algebras with Double Demi-pseudocomplementation and Others
|Keywords||double demi-pseudocomplemented lattice Ockham algebra congruence subdirectly irreducible|
In this thesis, we are mostly concerned with two subclasses of the class of Ockhams algebras with double demi-pseudocomplementation, namely the class of Ockham algebras with balanced double demi-pseudocomplementation and the class of de Morgan algebras with double demi-pseudocomplementation. We say that an algebra (L;∧,∨,*,+,f,0,1) is an Ockham algebras with balanced double demi-pseudocomplementation (shortly, bddpO-algebra) if (L;∧,∨,*,+,0,1) is a double demi-pseudocomplemented lattice with a dual endomorphism f such that [f(x)*=[f(x)]+=f2(x), f(x*)=x** and f(x+)=x++ for any x∈L. By a de Morgan algebras with double demi-pseudocomplementation (shortly, ddpM-algebra), we mean a double demi-pseudocomplemented-lattice (L;∧,∨,*,+,0,1) together with a de Morgan operation(?) such that x*(?)=x(?)*, x+(?)=x(?)+ and x*+=x+*.The main results in this thesis are to characterize congruences and the subdirectly irreducibilities of bddpO-algebras and ddpM-algebras. At the end of the thesis, we describe the boolean congruences and boolean ideals of the balanced pseudocomplemented Ockham algebras.