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Statements

Subject Item
n2:RIV%2F61989592%3A15310%2F11%3A10224904%21RIV12-MSM-15310___
rdf:type
n3:Vysledek skos:Concept
dcterms:description
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.
dcterms:title
Properties of relatively pseudocomplemented directoids Properties of relatively pseudocomplemented directoids
skos:prefLabel
Properties of relatively pseudocomplemented directoids Properties of relatively pseudocomplemented directoids
skos:notation
RIV/61989592:15310/11:10224904!RIV12-MSM-15310___
n3:predkladatel
n7:orjk%3A15310
n4:aktivita
n6:Z
n4:aktivity
Z(MSM6198959214)
n4:cisloPeriodika
1
n4:dodaniDat
n14:2012
n4:domaciTvurceVysledku
n5:8866791 n5:9055819 n5:6253806
n4:druhVysledku
n13:J
n4:duvernostUdaju
n19:S
n4:entitaPredkladatele
n17:predkladatel
n4:idSjednocenehoVysledku
224686
n4:idVysledku
RIV/61989592:15310/11:10224904
n4:jazykVysledku
n18:eng
n4:klicovaSlova
directoid, relatively pseudocomplemented directoid, congruence distributivity, 3-permutability, residuated structure, adjointness property, variety
n4:klicoveSlovo
n12:residuated%20structure n12:directoid n12:congruence%20distributivity n12:3-permutability n12:relatively%20pseudocomplemented%20directoid n12:adjointness%20property n12:variety
n4:kodStatuVydavatele
CZ - Česká republika
n4:kontrolniKodProRIV
[F0EBD86C4B51]
n4:nazevZdroje
Mathematica Bohemica
n4:obor
n8:BA
n4:pocetDomacichTvurcuVysledku
3
n4:pocetTvurcuVysledku
3
n4:rokUplatneniVysledku
n14:2011
n4:svazekPeriodika
136
n4:tvurceVysledku
Kolařík, Miroslav Švrček, Filip Chajda, Ivan
n4:zamer
n16:MSM6198959214
s:issn
0862-7959
s:numberOfPages
15
n15:organizacniJednotka
15310