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 J. S. Ratti and Y. F. Lin. 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
such that is left multiplicative and
is right multiplicative.