A characterization of pseudo-orders in the ring Z(n)
Partially ordered sets are widely studied in algebra. The theory of lattice-ordered and partially-ordered rings is an important case. In this paper, we consider a more general relation: pseudo orders, which are relations that are reflexive and antisymmetric, but are not necessarily transitive. Analogously to partially-ordered rings, we study pseudo-ordered rings. We present a general characterization for pseudo-ordered rings, and then we focus on a specific structure: the ring [special characters omitted]. Having the constraints of this ring, we are able to give the conditions under which [special characters omitted] can be pseudo-ordered.
Vargas, Jorge Ivan, "A characterization of pseudo-orders in the ring Z(n)" (2009). ETD Collection for University of Texas, El Paso. AAI1473898.