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Algebraic Aspects of Relatively Pseudocomplemented Posets

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CHAJDA Ivan LANGER Helmut PASEKA Jan

Rok publikování 2020
Druh Článek v odborném periodiku
Časopis / Zdroj Order-A Journal on the Theory of Ordered Sets and its Applications
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://doi.org/10.1007/s11083-019-09488-1
Doi http://dx.doi.org/10.1007/s11083-019-09488-1
Klíčová slova Relative pseudocomplementation; Poset; Hilbert algebra; Congruence; Convex poset; Dedekind-MacNeille completion; Glivenko equivalence; Category
Popis In Chajda and Langer (Math. Bohem. 143, 89-97, 2018) the concept of relative pseudocomplementation was extended to posets. We introduce the concept of a congruence in a relatively pseudocomplemented poset within the framework of Hilbert algebras and we study under which conditions the quotient structure is a relatively pseudocomplemented poset again. This problem is solved e.g. for finite or linearly ordered posets. We characterize relative pseudocomplementation by means of so-called L-identities. We investigate the category of bounded relatively pseudocomplemented posets. Finally, we derive certain quadruples which characterize bounded Hilbert algebras and bounded relatively pseudocomplemented posets up to isomorphism using Glivenko equivalence and implicative semilattice envelope of Hilbert algebras.
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