Displaying 161 – 180 of 445

Showing per page

Hausdorff ’s theorem for posets that satisfy the finite antichain property

Uri Abraham, Robert Bonnet (1999)

Fundamenta Mathematicae

Hausdorff characterized the class of scattered linear orderings as the least family of linear orderings that includes the ordinals and is closed under ordinal summations and inversions. We formulate and prove a corresponding characterization of the class of scattered partial orderings that satisfy the finite antichain condition (FAC).  Consider the least class of partial orderings containing the class of well-founded orderings that satisfy the FAC and is closed under the following operations: (1)...

Ideals in distributive posets

Cyndyma Batueva, Marina Semenova (2011)

Open Mathematics

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.

Currently displaying 161 – 180 of 445