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The identities of additive binary arithmetics

By Anton A. Klyachko and Ekaterina V. Menshova

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.Comment: 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 don

Topics: Computer Science - Discrete Mathematics, Mathematics - Group Theory, Mathematics - Rings and Algebras, 08A70
Year: 2012
OAI identifier: oai:arXiv.org:1102.5555
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