International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 1, Pages 205-207
doi:10.1155/S0161171289000256
Abstract
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.