Structures paragraduées (groupes, anneaux, modules). III. (Paragraded structures (groups, rings, modules). III) (Q1821133)

[For Parts I and II see the preceding reviews.] Paragraded rings are introduced as rings \((A,+,.)\) equipped with a paragraduation \(\pi\) such that for any x,y\(\in \Delta\) there is a \(z\in \Delta\) such that \(A_ xA_ y\subset A_ z\). From a semihomogeneous point of view an explicit characterization of paragraded rings is formulated by a list of 5 conditions. Paraneids, extraneids, quasineids, paragraded modules, extragraded modules are defined as well.