CAYLEY-SYMMETRIC SEMIGROUPS

Title & Authors
CAYLEY-SYMMETRIC SEMIGROUPS
Zhu, Yongwen;

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 $\small{S_{\alpha}}$ is Cayley-symmetric if and only if each $\small{S_{\alpha}}$ 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;
Language
English
Cited by
1.
GENERALIZED CAYLEY GRAPHS OF RECTANGULAR GROUPS,;

대한수학회보, 2015. vol.52. 4, pp.1169-1183
1.
On transitive generalized Cayley graphs of semigroups, Semigroup Forum, 2016, 93, 2, 247
2.
GENERALIZED CAYLEY GRAPHS OF RECTANGULAR GROUPS, Bulletin of the Korean Mathematical Society, 2015, 52, 4, 1169
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