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CAYLEY-SYMMETRIC SEMIGROUPS
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 Title & Authors
CAYLEY-SYMMETRIC SEMIGROUPS
Zhu, Yongwen;
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 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 is Cayley-symmetric if and only if each 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 crossref(new window)
1.
On transitive generalized Cayley graphs of semigroups, Semigroup Forum, 2016, 93, 2, 247  crossref(new windwow)
2.
GENERALIZED CAYLEY GRAPHS OF RECTANGULAR GROUPS, Bulletin of the Korean Mathematical Society, 2015, 52, 4, 1169  crossref(new windwow)
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