The identities of additive binary arithmetics (Q426806)

Summary: Operations of arbitrary arity expressible via addition modulo \(2^n\) and bitwise addition modulo 2 admit a simple description. The identities connecting these two additions have a finite basis. Moreover, the universal algebra \(\mathbb{Z}/2^n\mathbb{Z}\) with these two operations is rationally equivalent to a nilpotent ring and, therefore, generates a Specht variety.