Abstract
In this paper, we introduce the concept of clean semiring as a generalization of clean ring. A semiring is said to be clean if its every nonzero element can be written as the sum of an idempotent and a unit. We study the notion of clean semiring and obtain some important characterizations of clean semiring. We also study the notion of exchange semiring and find out the connenction between clean semiring and exchange semiring.
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Acknowledgements
D. Das is grateful to UGC, India for providing financial support as Junior Research Fellow (JRF). The authors are thankful to the anonymous referee for making some useful comments and suggestions which have definitely improved the paper.
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Kar, S., Das, D. Clean semiring. Beitr Algebra Geom 64, 197–207 (2023). https://doi.org/10.1007/s13366-022-00628-0
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DOI: https://doi.org/10.1007/s13366-022-00628-0