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Linear and Multilinear Algebra Volume 60, 2012 - Issue 5
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Original Articles

On semigroups and semirings of nonnegative matrices

Adel N. Alahmadi Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
,
Yousef Alkhamees Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
&
S.K. Jain Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Mathematics, King Saud University, Riyadh, Saudi Arabia; Department of Mathematics, Ohio University, Athens, OH 45701, USACorrespondence[email protected]
Pages 595-598 | Received 21 Jul 2011, Accepted 17 Aug 2011, Published online: 10 Oct 2011
 
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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.

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Acknowledgements

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

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