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
1Lipetsk State Technical University, Lipetsk 398055, Russia
2Department of Mathematics, University of Haifa, Haifa 31905, Israel
Received 22 July 2001
Copyright © 2002 Sam L. Blyumin and Jonathan S. Golan. 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.
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.