中文摘要：

设5是半群，A是S-系．首先给出了A的子系是极大子系的充分必要条件；其次利用所定义的B关系，证明了A的非空子集L是A的极大子系的充分必要条件是A＼L是A的（极大）B-类；最后，定义了C-子系的概念，讨论了其性质，并利用C-子系刻画了一类S-系．证明了S-系不包含极大子系当且仅当每一个循环子系是C-子系．从而Imrich Fabrici关于半群不包含极大（左）理想的主要结论就是本文的推论．

英文摘要：

Let S be a semigroup and let A be an S-act. Some necessary and sufficient conditions that S-subacts of A are maximal S-subacts are given. A relation B which is similar to the Green relation in semigroups is defined. By the relation B, it is proved that a non-empty set L of A is a maximal S-subact if and only if A／L is a （maximal） B-class. Finally, the concept of a C-subact is defined, some properties of C-subacts are discussed, and it is proved that A contains no maximal S-subacts if and only if every cyclic S-subact of A is a C-subact. Consequently, the results obtained by Imrich Fabrici that semigroups contain no maximal （left） ideals are the corollary of this paper.