ON REES MATRIX REPRESENTATIONS OF ABUNDANT SEMIGROUPS WITH ADEQUATE TRANSVERSALS | Zendy

Zhen Lin Gao | Zendy; Xian Ge Liu | Zendy; Yan Jun Xiang | Zendy; He Zuo | Zendy

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ON REES MATRIX REPRESENTATIONS OF ABUNDANT SEMIGROUPS WITH ADEQUATE TRANSVERSALS

Author(s) -

Zhen Lin Gao,

Xian Ge Liu,

Yan Jun Xiang,

He Zuo

Publication year - 2009

Publication title -

communications of the korean mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.286

H-Index - 15

eISSN - 2234-3024

pISSN - 1225-1763

DOI - 10.4134/ckms.2009.24.4.481

Subject(s) - transversal (combinatorics) , mathematics , semigroup , matrix (chemical analysis) , pure mathematics , regular semigroup , bar (unit) , special classes of semigroups , algebra over a field , discrete mathematics , combinatorics , mathematical analysis , physics , composite material , materials science , meteorology

The concepts of ⁄-relation of a (i-)semigroup and "-adequate transversal of a (i-)abundant semigroup are deflned 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 representa- tions for abundant semigroups with adequate transversals by the above theories.

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