Displaying similar documents to “On Hilbert's irreducibility theorem”

Annihilators and deductive systems in commutative Hilbert algebras

Ivan Chajda, Radomír Halaš, Young Bae Jun (2002)

Commentationes Mathematicae Universitatis Carolinae

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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 Ded H of all deductive systems on H and every maximal deductive system is prime. Complements and relative complements of Ded H are characterized as the so called annihilators in H .

Remarks on commutative Hilbert algebras

Radomír Halaš (2002)

Mathematica Bohemica

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The paper shows that commutative Hilbert algebras introduced by Y. B. Jun are just J. C. Abbot’s implication algebras.