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Abstract. In this note we will investigate some particular classes of ideals in Hilbert algebras with supremum. We shall study the relation between $\alpha $-ideals and annihilator ideals in bounded Hilbert algebras with supremum. We shall introduce the class of $\sigma $-ideals and we will see that this class is strongly connected with the deductive systems. We will also characterize the bounded Hilbert algebras with supremum satisfying the Stone identity.
DOI: 10.14232/actasm-012-267-9
AMS Subject Classification
(1991): 05C38, 15A15; 05A15, 15A18
Keyword(s):
Hilbert algebras with supremum,
annihilators,
$\alpha $-ideals,
$\sigma $-ideals,
Stone identity
Received March 19, 2012, and in final form June 8, 2012. (Registered under 17/2012.)
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