CAJ | 학술논문

设 T X 是非空集合 X 上全变换半群，E 是 X 上非平凡的等价关系，R 是 X ／E 的横断面，则T E （X ，R）＝｛ f ∈ T X ：? x ，y ∈ X ，（x ，y）∈ E ?（ f （x），f （y））∈ E 且 f （R）? R｝是 T X 的子半群。本文赋予半群 T E （X ，R）自然偏序关系，通过构造映射的方法，刻画它的左相容元，给出充要条件。
설 T X 시비공집합 X 상전변환반군，E 시 X 상비평범적등개관계，R 시 X ／E 적횡단면，칙T E （X ，R）＝｛ f ∈ T X ：? x ，y ∈ X ，（x ，y）∈ E ?（ f （x），f （y））∈ E 차 f （R）? R｝시 T X 적자반군。본문부여반군 T E （X ，R）자연편서관계，통과구조영사적방법，각화타적좌상용원，급출충요조건。
Let T X be the full transformation semigroup on a nonempty set X ,E be a nontrivial equivalence relation on X and R be a cross‐section of X /E ,then T E (X ,R)= { f ∈ T X :? x ,y ∈ X ,(x ,y) ∈ E ? (f (x) ,f (y)) ∈ E and f (R)? R}is a subsemigroup of T X .By constructing suitable mappings ,all the left compatible elements were described in the transformation semigroup T E (X ,R) endowed with the natural partial order and a necessary and sufficient condition for these elements was given .