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The concept of Cayley-symmetric semigroups is introduced, and several equivalent conditions of a Cayley-symmetric semigroup are given so that an open problem proposed by Zhu [19] is resolved generally.
Furthermore, it is proved that a strong semilattice of self-decomposable semigroups Sα is Cayley-symmetric if and only if each Sα is Cayley- symmetric. This enables us to present more Cayley-symmetric semi- groups, which would be non-regular. This result extends the main re- sult of Wang [14], which stated that a regular semigroup is Cayley- symmetric if and only if it is a Clifford semigroup. In addition, we discuss Cayley-symmetry of Rees matrix semigroups over a semigroup or over a 0-semigroup.
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참고문헌 (20)
참고문헌 신청
A. V. Kelarev / 2002 / Directed graphs and combinatorial properties of semi-groups / J. Algebra 251 (1) : 16 ~ 26
A. V. Kelarev / 2002 / On undirected Cayley graphs / Australas. J. Combin 25 : 73 ~ 78
A. V. Kelarev / 2003 / A combinatorial property and Cayley graphs of semigroups / Semigroup Forum 66 (1) : 89 ~ 96
A. V. Kelarev / 2003 / Graph Algebras and Automata / Marcel Dekker, Inc
A. V. Kelarev / 2003 / On transitive Cayley graphs of groups and semigroups / European J. Combin 24 (1) : 59 ~ 72
A. V. Kelarev / 2002 / On undirected Cayley graphs / Australas. J. Combin 25 : 73 ~ 78
A. V. Kelarev / 2003 / A combinatorial property and Cayley graphs of semigroups / Semigroup Forum 66 (1) : 89 ~ 96
A. V. Kelarev / 2003 / Graph Algebras and Automata / Marcel Dekker, Inc
A. V. Kelarev / 2003 / On transitive Cayley graphs of groups and semigroups / European J. Combin 24 (1) : 59 ~ 72
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