Abstract
The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by McAlister and Blyth on split orthodox semigroups.
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Supported by National Natural Science Foundation of China of China (Grant No. 10961014); Natural Science Foundation of Jiangxi Province and the SF of Education Department of Jiangxi Province, China (Grant No. GJJ11388)
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Guo, X.J., Peng, T.T. Split quasi-adequate semigroups. Acta. Math. Sin.-English Ser. 28, 425–438 (2012). https://doi.org/10.1007/s10114-012-9068-8
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DOI: https://doi.org/10.1007/s10114-012-9068-8