# A NOTE ON FULLY IDEMPOTENT S-ACTS

• Accepted : 2013.08.21
• Published : 2013.09.25
• 30 6

#### Abstract

In this article we introduce the notion of fully idempotent acts and by this we give a characterization of commutative monoids over which all cyclic right acts are injective.

#### Keywords

idempotent;fully idempotent;right S-act

#### References

1. M. Kilp, U. Knauer and A. V. Mikhalev, Monoids, Acts and Categories, With Application to Wreath Product, Berlin; New York, 2000.
2. X. Zhang, U. Knauer and Y. Chen, Classification of monoids by injectivities I. C-injectivity, Semigroup Forum, 76 (2008), 169-176. https://doi.org/10.1007/s00233-007-9022-8