Abstract:

Let S be a monoid and I an ideal of S. Using the ideal I the condition (PI) is defined. The necessary and sufficient condition of cyclic act satisfying condition (PI) is given and the monoids over which every cyclic act has a (PI)-cover are investigated. If the ideal I equals to S, the condition (PI) and condition (P) are equivalent, so the main results in the reference are generalized.

Key words:  cyclic S-act; condition (P); cover