The identities of additive binary arithmetics
Discrete Mathematics
2020-07-22 v3 Group Theory
Rings and Algebras
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 finite basis. Moreover, the universal algebra with these two operations is rationally equivalent to a nilpotent ring and, therefore, generates a Specht variety.
Cite
@article{arxiv.1102.5555,
title = {The identities of additive binary arithmetics},
author = {Anton A. Klyachko and Ekaterina V. Menshova},
journal= {arXiv preprint arXiv:1102.5555},
year = {2020}
}
Comments
6 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm . V3: the easier direction of the proof of the main theorem is corrected and some minor changes are done