Representation of artinian partially ordered sets over semiartinian von Neuman regular algebras

Boolean algebras over partially ordered sets

Being the crossroads between Algebra, Topology, Logic, Set Theory and the Theory of Order; the class of Boolean algebras over partially ordered sets were look at as one of the sources, providing over time, new insights in Boolean algebras. Some constructions and their interconnections will be discussed, motivating along the way a list of open problems. Mathematics Subject Classification (MSC 20...

Tripled partially ordered sets

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

On Algebras Associated to Partially Ordered Sets

We continue the study [2] on sheaves of rings on finite posets. We present examples where the ring of global sections coincide with toric faces rings, quotients of a polynomial ring by a monomial ideal and algebras with straightening laws. We prove a rank-selection theorem which generalizes the well-known rank-selection theorem of Stanley–Reisner rings. Finally, we determine an explicit present...

Some Representation Theorems for Partially Ordered Sets

On Sums Over Partially Ordered Sets

We establish a general theorem for reducing sums of type ∑ y≥x g(y) where g is a mapping from a partially ordered set into an abelian group. Conclusions concern the Möbius function, the principle of inclusionexclusion, the Tutte polynomial and Crapo’s beta invariant.