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 Cayley-symmetric semigroups Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 409-419 https://doi.org/10.4134/BKMS.2015.52.2.409Published online March 31, 2015 Yongwen Zhu Yantai University Abstract : 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 \cite{Zhu-Cayley-2} is resolved generally. Furthermore, it is proved that a strong semilattice of self-decomposable semigroups $S_{\alpha}$ is Cayley-symmetric if and only if each $S_{\alpha}$ is Cayley-symmetric. This enables us to present more Cayley-symmetric semigroups, which would be non-regular. This result extends the main result of Wang \cite{wang}, 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. Keywords : generalized Cayley graph, Cayley-symmetric semigroup, strong semilattice of semigroups, self-decomposable MSC numbers : 05C25, 20M12, 20M17 Downloads: Full-text PDF