‎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...

this work is devoted to give a charcaterization of a pomonoid $s$such that all cyclic $s$-posets are regular injective.

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.

Let D be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On ZD we define a product and a coproduct, together with an internal product, that is, degree-preserving. With these operations ZD is a Hopf algebra, self-dual with respect to a scalar product which counts the number of pictures (in the sense of Zelevinsky) between two do...

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...

Fuzzy order congruences play an important role in studying the categoricalproperties of fuzzy posets. In this paper, the correspondence between the fuzzyorder congruences and the fuzzy order-preserving maps is discussed. We focus onthe characterization of fuzzy order congruences on the fuzzy poset in terms ofthe fuzzy preorders containing the fuzzy partial order. At last, fuzzy completecongruen...

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...

We study the set S nc(p, q) of annular non-crossing permutations of type B, and we introduce a corresponding set NC(p, q) of annular non-crossing partitions of type B, where p and q are two positive integers. We prove that the natural bijection between S nc(p, q) and NC (p, q) is a poset isomorphism, where the partial order on S nc(p, q) is induced from the hyperoctahedral group Bp+q, while NC ...