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Epigroups in which the relation of having the same pseudo-inverse is a congruence

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Abstract

The purpose of the paper is to find several characterizations of epigroups mentioned in the title. Some special cases are also considered.

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Acknowledgements

I would like to express my profound gratitude to Professor Shevrin. He not only proposed the question for direction of research but also offered many ideas of proofs in this paper (especially proofs of Theorem 3.1, Lemmas 2.6 and 4.2), making the text more concise and acceptable. Furthermore, he gave plenty of valuable remarks and suggestions that led to many improvements in the paper.

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Authors and Affiliations

  1. School of Sciences, Linyi University, Linyi, 276005, Shandong, P.R. China

    Jingguo Liu

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  1. Jingguo Liu
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Correspondence to Jingguo Liu.

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Communicated by Lev N. Shevrin.

Supported by Shandong Province Natural Science Foundation N0. ZR2010AL004.

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Liu, J. Epigroups in which the relation of having the same pseudo-inverse is a congruence. Semigroup Forum 87, 187–200 (2013). https://doi.org/10.1007/s00233-012-9462-7

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  • DOI: https://doi.org/10.1007/s00233-012-9462-7

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