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  • The concept of a relatively pseudocomplemented directoid was introduced recently by Ivan Chajda. It was shown that the class of relatively pseudocomplemented directoids forms a variety whose axiom system contains seven identities. The aim of this paper is three-fold. First we show that these identities are not independent and their independent subset is presented. Second, we modify the adjointness property known for relatively pseudocomplemented semilattices in the way which is suitable for relatively pseudocomplemented directoids. Hence, they can also be considered as residuated structures in a rather modified version. We also get two important congruence properties, namely congruence distributivity and 3-permutability valid in the variety V of relatively pseudocomplemented directoids. Then we show some basic results connected with subdirect irreducibility in V. Finally, we show another way how to introduce pseudocomplementation on directoids via relative pseudocomplementation.
  • The concept of a relatively pseudocomplemented directoid was introduced recently by Ivan Chajda. It was shown that the class of relatively pseudocomplemented directoids forms a variety whose axiom system contains seven identities. The aim of this paper is three-fold. First we show that these identities are not independent and their independent subset is presented. Second, we modify the adjointness property known for relatively pseudocomplemented semilattices in the way which is suitable for relatively pseudocomplemented directoids. Hence, they can also be considered as residuated structures in a rather modified version. We also get two important congruence properties, namely congruence distributivity and 3-permutability valid in the variety V of relatively pseudocomplemented directoids. Then we show some basic results connected with subdirect irreducibility in V. Finally, we show another way how to introduce pseudocomplementation on directoids via relative pseudocomplementation. (en)
Title
  • Properties of relatively pseudocomplemented directoids
  • Properties of relatively pseudocomplemented directoids (en)
skos:prefLabel
  • Properties of relatively pseudocomplemented directoids
  • Properties of relatively pseudocomplemented directoids (en)
skos:notation
  • RIV/61989592:15310/11:10224904!RIV12-MSM-15310___
http://linked.open...avai/predkladatel
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM6198959214)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 224686
http://linked.open...ai/riv/idVysledku
  • RIV/61989592:15310/11:10224904
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • directoid, relatively pseudocomplemented directoid, congruence distributivity, 3-permutability, residuated structure, adjointness property, variety (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [F0EBD86C4B51]
http://linked.open...i/riv/nazevZdroje
  • Mathematica Bohemica
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 136
http://linked.open...iv/tvurceVysledku
  • Chajda, Ivan
  • Kolařík, Miroslav
  • Švrček, Filip
http://linked.open...n/vavai/riv/zamer
issn
  • 0862-7959
number of pages
http://localhost/t...ganizacniJednotka
  • 15310
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