Geodesic
Relatively pseudocomplemented directoids
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 3, pp. 349-357 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called $p$-ideals.
The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called $p$-ideals.
Classification : 06A12, 06D15, 08B10
Keywords: directoid; relative pseudocomplementation; filter; congruence distributivity; congruence weak regularity 
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     author = {Chajda, Ivan},
     title = {Relatively pseudocomplemented directoids},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {349--357},
     year = {2009},
     volume = {50},
     number = {3},
     mrnumber = {2573409},
     zbl = {1212.06004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2009_50_3_a2/}
}
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Chajda, Ivan. Relatively pseudocomplemented directoids. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 3, pp. 349-357. http://geodesic.mathdoc.fr/item/CMUC_2009_50_3_a2/