In this paper, we establish the relation between one-sided ball potentials by means of radially singular operators in a spherical layer. Moreover, construct new Chern-type potentials.

We give a thorough structural analysis of the principal one-sided ideals arbitrary semigroups, and then apply this to full transformation semigroups symmetric inverse monoids. One-sided these naturally occur as transformations with restricted range or kernel.

We show that the quasiequational theory of a relatively congruence modular quasivariety of left R-modules is determined by a two-sided ideal in R together with a filter of left ideals. The two-sided ideal encodes the identities that hold in the quasivariety, while the filter of left ideals encodes the quasiidentities. The filter of left ideals defines a generalized notion of torsion. It follows...