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Congruence kernels of distributive PJP-semilattices

S. N. Begum, Abu Saleh Abdun Noor (2011)

Mathematica Bohemica

A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices.

Convex independence and the structure of clone-free multipartite tournaments

Darren B. Parker, Randy F. Westhoff, Marty J. Wolf (2009)

Discussiones Mathematicae Graph Theory

We investigate the convex invariants associated with two-path convexity in clone-free multipartite tournaments. Specifically, we explore the relationship between the Helly number, Radon number and rank of such digraphs. The main result is a structural theorem that describes the arc relationships among certain vertices associated with vertices of a given convexly independent set. We use this to prove that the Helly number, Radon number, and rank coincide in any clone-free bipartite tournament. We...

Convex isomorphisms of directed multilattices

Ján Jakubík, Mária Csontóová (1993)

Mathematica Bohemica

By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.

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