On some properties of directoids

Chajda I;Gil Férez J;GIUNTINI, ROBERTO;Kolarik M;LEDDA, ANTONIO;PAOLI, FRANCESCO

2015-01-01

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Abstract

We study some properties of directoids and their expansions by additional signature, including bounded involutive directoids and complemented directoids. Among other results, we provide a shorter proof of the direct decomposition theorem for bounded involutive directoids given in Chajda and Langer (Directoids. An algebraic approach to ordered sets. Heldermann Verlag, Lemgo 2011); we present a description of central elements of complemented directoids; we show that the variety of directoids, as well as its expansions mentioned above, all have the strong amalgamation property.