Convolution rings

The notion of a convolution type is introduced. Imposing such a type on a ring gives the corresponding convolution ring. Under this umbrella, a wide variety of ring constructions can be covered, including polynomials, matrices, incidence algebras, necklace rings, group rings and quaternion rings. Here the influence of the convolution type on the corresponding convolution ring is investigated, in particular on the existence of homomorphisms and ideals.