Abstract
In this paper, we study the concept of strongly clean semiring. Let S be a semiring. An element \(a\in S\) is called strongly clean if \(a = e + u\) with e an idempotent in S and u a unit in S such that \(eu=ue\). A semiring S is said to be strongly clean if every nonzero element of S is strongly clean. We mainly study the notion of strongly clean semiring and obtain some important characterizations of strongly clean semiring in connection with exchange semiring, antisimple semiring and inverse semiring.
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Acknowledgements
D.Das is grateful to UGC, India for providing financial support as Senior Research Fellow (SRF).
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The statement explaining the relevance of the work: Semirings are natural generalization of rings and bounded distributive lattices. The algebraic theory of strongly clean semiring generalizes the results of strongly clean ring. This results may be applied in different branches of mathematics, computer science, quantum physics and many other areas of science as semiring theory plays an important role in this areas of science.
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Das, D., Kar, S. Strongly Clean Semiring. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 94, 249–258 (2024). https://doi.org/10.1007/s40010-024-00875-x
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DOI: https://doi.org/10.1007/s40010-024-00875-x