We study noncommutative disc algebras associated to the free product of discrete subsemigroups of R +. These algebras are associated to generalized Cuntz algebras, which are shown to be simple and purely innnite. The nonself-adjoint subalgebras determine the semigroup up to isomorphism. Moreover, we establish a dilation theorem for contractive representations of these semigroups which yields a ...

In this paper, we introduced the concepts of roughness and fuzziness in ordered ternary semigroups. We proved that the lower and upper approximation of an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal) in an ordered ternary semigroup is an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal)....