# ON REES MATRIX REPRESENTATIONS OF ABUNDANT SEMIGROUPS WITH ADEQUATE TRANSVERSALS

• Gao, Zhen Lin (SCIENCE COLLEGE OF UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY) ;
• Liu, Xian Ge (SCIENCE COLLEGE OF UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY) ;
• Xiang, Yan Jun (SCIENCE COLLEGE OF UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY) ;
• Zuo, He Li (SCIENCE COLLEGE OF UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY)
• Published : 2009.10.31

#### Abstract

The concepts of *-relation of a ($\Gamma$-)semigroup and $\bar{\Gamma}$-adequate transversal of a ($\Gamma$-)abundant semigroup are defined in this note. Then we develop a matrix type theory for abundant semigroups. We give some equivalent conditions of a Rees matrix semigroup being abundant and some equivalent conditions of an abundant Rees matrix semigroup having an adequate transversal. Then we obtain some Rees matrix representations for abundant semigroups with adequate transversals by the above theories.

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