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The principal join property in demi-p-lattices. (English) Zbl 1150.06010
A demi-p-lattice is a bounded distributive lattice equipped with an additional unary operation, satisfying certain identities. Demi-p-lattices form a subvariety of the variety (equational class) of semi-De Morgan algebras.
An algebra \(L\) has the principal join property (PJP) if the join of any two principal congruences is again a principal congruence. The principal intersection property (PIP) is defined similarly.
The main result of this paper characterizes the demi-p-lattices with PJP, both algebraically and in terms of the dual Priestley spaces. An additional characterization is given for some special demi-p-lattices, called almost-p-lattices. Finally, it is proved that, in demi-p-lattices, PJP implies PIP.
MSC:
06D15 Pseudocomplemented lattices
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