The Identities of Additive Binary Arithmetics

Abstract

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.