A NEW CHARACTERIZATION OF ABSOLUTELY PO-PURE AND ABSOLUTELY PURE S-POSETS

Subpullbacks and Po-flatness Properties of S-posets

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...

Absolutely Rigid Systems and Absolutely Indecomposable Groups

We give a new proof that there are arbitrarily large indecomposable abelian groups; moreover, the groups constructed are absolutely indecomposable, that is, they remain indecomposable in any generic extension. However, any absolutely rigid family of groups has cardinality less than the partition cardinal κ(ω). Added December 2004: The proofs of Theorems 0.2 and 0.3 are not correct, and the clai...

On (po-)torsion free and principally weakly (po-)flat $S$-posets

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 ...

On Absolutely Continuous Transformations

A characterization of a pomonoid $S$ all of its cyclic $S$-posets are regular injective

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

Absolutely Secure Classical Cryptography

Fundamental problem of cryptography is to create more absolutely secure bits than the initially shared secret bits between two legitimate users. It is widely believed that this task can only be accomplished by quantum cryptosystems. We present a simple classical cryptosystem, which can fulfill this objective.