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International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 1, Pages 205-207

On anti-commutative semirings

Department of Mathematics, University of South Florida, Tampa 33620, Florida, USA

Received 28 March 1988

Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An anticommutative semiring is completely characterized by the types of multiplications that are permitted. It is shown that a semiring is anticommutative if and only if it is a product of two semirings R1 and R2 such that R1 is left multiplicative and R2 is right multiplicative.