Abstract
Monzo characterized semigroups which are semilattices of rectangular bands and groups of exponent 2. Recently, Ara\(\acute{\text {u}}\)jo and Kinyon gave a new characterization for that class of semigroups and in the end of their paper asked a number of questions. In this note we characterize semilattices of rectangular bands and groups, thus generalizing Ara\(\acute{\text {u}}\)jo and Kinyon’s result and providing partial solutions to the questions they ask.
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References
Petrich, M., Reilly, N.R.: Completely Regular Semigroups. Wiley, New York (1999)
Monzo, R.A.R.: Semilattices of rectangular bands and groups of order 2 (2013). arXiv:1301.0828
Araújo, J.P., Kinyon, M.: A natural characterization of semilattices of rectangular bands and groups of exponent two. Semigroup Forum 91, 295–298 (2015)
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Acknowledgments
The authors are particularly grateful to professor V. Gould for her helpful comments and suggestions. The authors also thank referees for an unusually careful reading of the paper and for proposing modifications which led to a substantial improvement of this paper. The authors are supported by a Grant of Natural Science Foundation of China (11571278) and a Grant of Natural Science Foundation of Shannxi Province (2015JQ1020).
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Communicated by Victoria Gould.
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Shao, Y., Ren, M. On semilattices of rectangular bands and groups. Semigroup Forum 93, 201–204 (2016). https://doi.org/10.1007/s00233-016-9807-8
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DOI: https://doi.org/10.1007/s00233-016-9807-8