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http://dx.doi.org/10.4134/BKMS.2015.52.2.409

CAYLEY-SYMMETRIC SEMIGROUPS  

Zhu, Yongwen (School of Mathematics and Information Science Yantai University)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 409-419 More about this Journal
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 [19] 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 semi-groups, which would be non-regular. This result extends the main result 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.
Keywords
generalized Cayley graph; Cayley-symmetric semigroup; strong semilattice of semigroups; self-decomposable;
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