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...

‎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 (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...

In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are ...

this paper is devoted to the study of products of classes of right $s$-posets possessing one of the flatness properties and preservation of such properties under products. specifically, we characterize a pomonoid $s$ over which its nonempty products as right $s$-posets satisfy some known flatness properties. generalizing this results, we investigate products of right $s$-posets satisfying condi...

This paper is devoted to the study of products of classes of right $S$-posets possessing one of the flatness properties and preservation of such properties under products. Specifically, we characterize a pomonoid $S$ over which its nonempty products as right $S$-posets satisfy some known flatness properties. Generalizing this results, we investigate products of right $S$-posets satisfying Condi...

Let C be a class of ordered algebras of a given fixed type τ . Associated with the type is a first order language Lτ , which must also contain a binary predicate to be interpreted by the ordering in members of C. One can then ask the question, when is the class C axiomatisable by sentences of Lτ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a ...

Let C be a class of ordered algebras of a given fixed type τ . Associated with the type is a first order language Lτ , which must also contain a binary predicate to be interpreted by the ordering in members of C. One can then ask the question, when is the class C axiomatisable by sentences of Lτ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a ...