The identities of additive binary arithmetics
  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 finite basis. Moreover, the universal algebra with these two operations is rationally equivalent to a nilpotent ring and, therefore, generates a Specht variety. 
Anton A. Klyachko and Ekaterina V. Menshova
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