Abundant Semigroups Which Are Disjoint Unions of Multiplicative Adequate Transversals
Received:December 20, 2011  Revised:March 01, 2012
Key Word: abundant semigroup   adequate transversal   multiplicative adequate transversal   [left   right] normal band.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10961014), the Natural Science Foundation of Jiangxi Province (Grant No.2014BAB201009) and the Science Foundation of Education Department of Jiangxi Province (Grant No.GJJ11388).
Author NameAffiliation
Haijun LIU Department of Mathematics, Jiangxi Normal University, Jiangxi 330022, P. R. China 
Xiaojiang GUO Department of Mathematics, Jiangxi Normal University, Jiangxi 330022, P. R. China 
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Abstract:
      The aim of this paper is to study abundant semigroups which are disjoint unions of multiplicative adequate tranversals. After obtaining some properties of such semigroup, we prove that a semigroup is a disjoint union of multiplicative adequate transversals if and only if it is isomorphic to the direct product of a rectangular band and an adequate semigroup.
Citation:
DOI:10.3770/j.issn:2095-2651.2013.03.005
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