Ideal systems and lattice theory.
We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a characterization of n-normal meet semilattices with zero, thus generalizing a known result for lattices with zero.
Every incidence structure (understood as a triple of sets , ) admits for every positive integer an incidence structure where () consists of all independent -element subsets in () and is determined by some bijections. In the paper such incidence structures are investigated the ’s of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets and .