On anti-commutative semirings - J. S. Ratti; Y. F. Lin (International Journal of Mathematics and Mathematical Sciences)
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.