On semigroups and semirings of nonnegative matrices

Abstract

We characterize a finite cyclic semigroup of nonnegative matrices by generalizing a result known for the special case in which the semigroup is a group. We also characterize semirings S of nonnegative matrices A with diag A ⩾ I whose multiplicative semigroup S − {0} is cyclic.

Keywords:

• semiring
• semigroup
• group inverse
• Drazin inverse

AMS Subject Classifications::

• Primary: 15A09
• Seondary: 05B20

Acknowledgements

The authors would like to thank the referee for his/her careful reading of the manuscript and suggestions.