| CHAJDA, Ivan, Helmut LANGER a Jan PASEKA. Algebraic Aspects of Relatively Pseudocomplemented Posets. Order-A Journal on the Theory of Ordered Sets and its Applications. Dordrecht: Springer, 2020, roč. 37, č. 1, s. 1-29. ISSN 0167-8094. Dostupné z: https://dx.doi.org/10.1007/s11083-019-09488-1. |
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@article{1693381,
author = {Chajda, Ivan and Langer, Helmut and Paseka, Jan},
article_location = {Dordrecht},
article_number = {1},
doi = {http://dx.doi.org/10.1007/s11083-019-09488-1},
keywords = {Relative pseudocomplementation; Poset; Hilbert algebra; Congruence; Convex poset; Dedekind-MacNeille completion; Glivenko equivalence; Category},
language = {eng},
issn = {0167-8094},
journal = {Order-A Journal on the Theory of Ordered Sets and its Applications},
title = {Algebraic Aspects of Relatively Pseudocomplemented Posets},
url = {https://doi.org/10.1007/s11083-019-09488-1},
volume = {37},
year = {2020}
}
TY - JOUR
ID - 1693381
AU - Chajda, Ivan - Langer, Helmut - Paseka, Jan
PY - 2020
TI - Algebraic Aspects of Relatively Pseudocomplemented Posets
JF - Order-A Journal on the Theory of Ordered Sets and its Applications
VL - 37
IS - 1
SP - 1-29
EP - 1-29
PB - Springer
SN - 01678094
KW - Relative pseudocomplementation
KW - Poset
KW - Hilbert algebra
KW - Congruence
KW - Convex poset
KW - Dedekind-MacNeille completion
KW - Glivenko equivalence
KW - Category
UR - https://doi.org/10.1007/s11083-019-09488-1
L2 - https://doi.org/10.1007/s11083-019-09488-1
N2 - 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.
ER -
CHAJDA, Ivan, Helmut LANGER a Jan PASEKA. Algebraic Aspects of Relatively Pseudocomplemented Posets. \textit{Order-A Journal on the Theory of Ordered Sets and its Applications}. Dordrecht: Springer, 2020, roč.~37, č.~1, s.~1-29. ISSN~0167-8094. Dostupné z: https://dx.doi.org/10.1007/s11083-019-09488-1.
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