The Identities of Additive Binary Arithmetics

Anton A. Klyachko, Ekaterina V. Menshova


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.

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