International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 8, Pages 453-458
doi:10.1155/S0161171202007792
One-sided complements and solutions of the equation aXb=c in semirings
Sam L. Blyumin1
and Jonathan S. Golan2
1Lipetsk State Technical University, Lipetsk 398055, Russia
2Department of Mathematics, University of Haifa, Haifa 31905, Israel
Abstract
Given multiplicatively-regular elements a and b in a semiring R, and given an element c of R, we find a complete set of solutions to the equation aXb=c. This result is then extended to equations over matrix semirings.