# CAYLEY-SYMMETRIC SEMIGROUPS

• Zhu, Yongwen (School of Mathematics and Information Science Yantai University)
• Published : 2015.03.31

#### 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.

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#### Cited by

1. On transitive generalized Cayley graphs of semigroups vol.93, pp.2, 2016, https://doi.org/10.1007/s00233-015-9762-9
2. GENERALIZED CAYLEY GRAPHS OF RECTANGULAR GROUPS vol.52, pp.4, 2015, https://doi.org/10.4134/BKMS.2015.52.4.1169