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On quasi completely regular semirings

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Abstract

We extend the concepts of a completely π-regular semigroup and a GV semigroup to semirings and find a semiring analogue of a structure theorem on GV semigroups. We also show that a semiring S is quasi completely regular if and only if S is an idempotent semiring of quasi skew-rings.

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Acknowledgements

The authors are indebted to Dr. M.K. Sen for his valuable suggestions. The authors are grateful to the anonymous referee for his or her valuable suggestions that helped to improve the presentation of this paper; they are also thankful to Prof. M.V. Volkov for editing the article.

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Authors and Affiliations

  1. Department of Mathematics, University of Burdwan, Golapbag, Burdwan, 713104, India

    S. K. Maity & R. Ghosh

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  1. S. K. Maity
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  2. R. Ghosh
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Correspondence to S. K. Maity.

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Communicated by Mikhail Volkov.

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Maity, S.K., Ghosh, R. On quasi completely regular semirings. Semigroup Forum 89, 422–430 (2014). https://doi.org/10.1007/s00233-014-9579-y

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  • DOI: https://doi.org/10.1007/s00233-014-9579-y

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