‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...

In this paper the notion of Rees short exact sequence for S-posets is introduced, and we investigate the conditions for which these sequences are left or right split. Unlike the case for S-acts, being right split does not imply left split. Furthermore, we present equivalent conditions of a right S-poset P for the functor Hom(P;-) to be exact.

in (golchin a. and rezaei p., subpullbacks and flatness properties of s-posets. comm. algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right -posets  over a pomonoid  that can be described by surjectivity of  corresponding to certain (sub)pullback diagrams and new properties such as  and  were discovered. in this article first of all we describe po-flatness propertie...

Spines T a tree on a signed ground set V = V− t V. Spine on T = directed and labeled tree S such that • the labels of the nodes of S form a partition of the signed ground set V, • at a node labeled by U = U− t U, the source label sets of the incoming arcs are subsets of distinct connected components of TrU−, and the sink label sets of the outgoing arcs are subsets of distinct connected componen...

In this paper, we investigate the Möbius function μS associated to a (locally finite) poset arising from a semigroup S of Zm. We introduce and develop a new approach to study μS by using the Hilbert series of S. The latter enables us to provide formulas for μS when S belongs to certain families of semigroups. Finally, a characterization for a locally finite poset to be isomorphic to a semigroup...

A subset S of a poset (partially ordered set) is convex if and only if S contains every poset element which is between any two elements in S. Poset convex subsets arise in applications that involve precedence constraints, such as in project scheduling, production planning, and assembly line balancing. We give a strongly polynomial time algorithm which, given a poset and element weights (of arbi...

in this paper we study the notions of cogenerator and subdirectlyirreducible in the category of s-poset. first we give somenecessary and sufficient conditions for a cogenerator $s$-posets.then we see that under some conditions, regular injectivityimplies generator and cogenerator. recalling birkhoff'srepresentation theorem for algebra, we study subdirectlyirreducible s-posets and give this theo...

In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theo...

For any graded poset P, we define a new graded poset, E(P ), whose elements are the edges in the Hasse diagram of P. For any group, G, acting on the boolean algebra, Bn, we conjecture that E(Bn/G) is Peck. We prove that the conjecture holds for “common cover transitive” actions. We give some infinite families of common cover transitive actions and show that the common cover transitive actions a...

We examine the lattice of all order congruences of a finite poset from the viewpoint of combinatorial algebraic topology. We will prove that the order complex of the lattice of all nontrivial order congruences (or order-preserving partitions) of a finite n-element poset P with n ≥ 3 is homotopy equivalent to a wedge of spheres of dimension n − 3. If P is connected, then the number of spheres is...