Abstract
The most powerful formulation of the Central Sets Theorem in an arbitrary semigroup was proved in the work of De, Hindman, and Strauss. The sets which satisfy the conclusion of the above Central Sets Theorem are called C-sets. The original Central Sets Theorem was extended by J. McLeod for adequate commutative partial semigroups. In this work, we will extend the Central Sets Theorem obtained by taking all possible adequate sequences in a commutative adequate partial semigroup. We shall also discuss a sufficient condition for being a set C-set in our context.
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Acknowledgements
The author would like to thank the referee for careful reading of the draft and enormous valuable suggestions to the improvements of the article. She also thanks her advisor Prof. Dibyendu De for his guidance and suggestions. Finally, the author acknowledges support received from the UGC-NET research grant.
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Communicated by Anthony To-Ming Lau.
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Ghosh, A. A generalized central sets theorem in partial semigroups. Semigroup Forum 100, 169–179 (2020). https://doi.org/10.1007/s00233-018-9977-7
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DOI: https://doi.org/10.1007/s00233-018-9977-7