Processes can be seen as relations extended in time. In this paper we want to investigate this observation by deriving an ordered category of processes. We model processes as co-algebras of a relator on Dedekind category up to bisimilarity. On those equivalence classes we define a lower semi-lattice structure and a monotone composition operation.

We obtain a criterion for quasiconvexity of a subgroup of an amalgamated free product of two word hyperbolic groups along a virtually cyclic subgroup. The result provides a method of constructing new word hyperbolic group in class (Q), that is such that all their finitely generated subgroups are quasiconvex. It is known that free groups, hyperbolic surface groups and most 3-dimensional Kleinian...

Exponential equations in free groups were studied initially by Lyndon and Schützenberger [26] and then by Comerford and Edmunds [5]. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper we show that for finite systems of quadratic exponential equations...

The motivation of this article is to define approximately near rings, some types $N$-groups, ideals, and rings all descriptive cosets. Moreover, properties these algebraic structures are given. Furthermore, near-ring homomorphisms introduced their investigated.