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Algebra and its Applications pp 225–239Cite as

\(\Gamma \)-Semigroups: A Survey

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 174))

Abstract

The concept of \(\Gamma \)-semigroup is a generalization of semigroup. Let S and \(\Gamma \) be two nonempty sets. S is called \(\Gamma \)-semigroup if there exists a mapping \(S\times \Gamma \times S\longrightarrow S\), written as \((a, \alpha , b)\longrightarrow a\alpha b\), satisfying the identity \( (a\alpha b)\beta c\) \(=\) \(a\alpha (b\beta c) \) for all \(a, b, c\in S\) and \( \alpha , \beta \in \Gamma \). This article is a survey of some works published by different authors on \(\Gamma \)-semigroups.

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Acknowledgments

The authors would like to thank the learned referee for his valuable suggestions that improved the praper.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Calcutta, Calcutta, India

    M. K. Sen

  2. Sovarani Memorial College, Jagathballavpur, India

    S. Chattopadhyay

Authors
  1. M. K. Sen
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  2. S. Chattopadhyay
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Correspondence to M. K. Sen .

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Editors and Affiliations

  1. The Ohio State University, Department of Mathematics, The Ohio State University, LIMA, Ohio, USA

    Syed Tariq Rizvi

  2. Aligarh Muslim University, Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Asma Ali

  3. University of Messina, Department of Mathematics & Computer Sci University of Messina, Messina, Italy

    Vincenzo De Filippis

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Sen, M.K., Chattopadhyay, S. (2016). \(\Gamma \)-Semigroups: A Survey. In: Rizvi, S., Ali, A., Filippis, V. (eds) Algebra and its Applications. Springer Proceedings in Mathematics & Statistics, vol 174. Springer, Singapore. https://doi.org/10.1007/978-981-10-1651-6_12

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