Abstract. In this paper, we introduce SR-additive codes as a general- ization of the classes of ZprZps and Z2Z2[u]-additive codes, where S is an R-algebra and an SR-additive code is an R-submodule of S R . In particular, the de nitions of bilinear forms, weight functions and Gray maps on the classes of ZprZps and Z2Z2[u]-additive codes are generalized to SR-additive codes. Also the singleton bound for SR-additive codes and some results on one weight SR-additive codes are given. Among other important results, we obtain the structure of SR-additive cyclic codes. As some results of the theory, the structure of cyclic Z2Z4, ZprZps , Z2Z2[u], (Z2)(Z2+uZ2+u2Z2), (Z2+uZ2)(Z2+uZ2+u2Z2), (Z2)(Z2+uZ2+vZ2) and (Z2 + uZ2)(Z2 + uZ2 + vZ2)-additive codes are presented.
