Annihilators and deductive systems in commutative Hilbert algebras
نویسندگان
چکیده
The properties of deductive systems in Hilbert algebras are treated. If a Hilbert algebra H considered as an ordered set is an upper semilattice then prime deductive systems coincide with meet-irreducible elements of the lattice DedH of all deductive systems on H and every maximal deductive system is prime. Complements and relative complements of DedH are characterized as the so called annihilators in H.
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