[C(E),C_a(E)]中的唯一原子

A Unique Atom in [C(E),C_a(E)]

对于集会 Ｘ上的任一非平凡等价关系 Ｅ，本文考察了半群 ＴＥ（Ｘ）上的同余Ｃ．（Ｅ），并证明了Ｃ*（Ｅ）是ＴＥ（Ｘ）的同余格的完全子格［Ｃ（Ｅ），Ｃ．（Ｅ）］中的唯一原子．

A congruence C. (E) on the semigroup TE(X) is observed in this paper where E is an arbitrary non-trivial equivalence on the set X. It is proved that C. (E) is a unique atom in the complete sublattice [C(E),C. (E)] of the congruence lattice of T.(X).