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Notes on bounded Hilbert algebras with supremum

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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 α-ideals and annihilator ideals in bounded Hilbert algebras with supremum. We shall introduce the class of σ-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.

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Acknowledgement

The author would like to thank the anonymous referee for his/her helpful suggestions that helped to improve the readability of the paper.

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Authors and Affiliations

  1. Departamento de Matemáticas, CONICET and Universidad Nacional del Centro, Pinto 399, 7000, Tandil, Argentina

    Sergio A. C

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  1. Sergio A. C
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Correspondence to Sergio A. C.

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Communicated by L. Zαdori

This research was supported by the CONICET under grant PIP 112-200801-02543.

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C, S.A. Notes on bounded Hilbert algebras with supremum. ActaSci.Math. 80, 3–19 (2014). https://doi.org/10.14232/actasm-012-267-9

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  • DOI: https://doi.org/10.14232/actasm-012-267-9

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