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Quasi-decompositions and quasidirect products of Hilbert algebras. (English) Zbl 07438421

Analyzing the direct decomposition of Hilbert algebras into two components, E. L. Marsden [J. Nat. Sci. Math. 14, 23–34 (1974; Zbl 0334.02028)] showed that if a Hilbert algebra \((A,\longrightarrow, 1)\) is isomorphic to a direct product of Hilbert algebras, then each factor is isomorphic to a filter of A. In this paper, the author deals with some special cases of this problem, but deals, instead of direct decompositions of a Hilbert algebra, with its so called quasi-direct decompositions which are introduced by himself in [Contrib. Gen. Algebra 16, 25–34 (2005; Zbl 1082.03056)].

MSC:

03G25 Other algebras related to logic
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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