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Keywords:
directoid; relative pseudocomplementation; filter; congruence distributivity; congruence weak regularity
directoid; relative pseudocomplementation; filter; congruence distributivity; congruence weak regularity
Summary:
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.
References:
[1] Chajda I.: Pseudocomplemented directoids. Comment. Math. Univ. Carolin. 49 (2008), 533--539. MR 2493936
[2] Chajda I., Halaš R., Kühr J.: Semilattice Structures. Heldermann Verlag, Lemgo (Germany), 2007, 228pp, ISBN 978-3-88538-230-0. MR 2326262
[3] Ježek J., Quackenbush R.: Directoids: algebraic model of up-directed sets. Algebra Universalis 27 (1990), 49--69. DOI 10.1007/BF01190253 | MR 1025835
[4] Jones G.T.: Pseudo-complemented semi-lattices. Ph.D. Thesis, Univ. of California, Los Angeles, 1972.
[5] Snášel V.: $łambda$-lattices. Math. Bohem. 122 (1997), 267--272. MR 1600648
[6] Chajda I., Rachůnek J.: Forbidden configurations for distributive and modular ordered sets. Order 5 (1989), 407--423. DOI 10.1007/BF00353659 | MR 1010389
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