Abundant Semigroups With the *-ideal Retraction Property
Ranran Cui · Journal of Convergence Information Technology · 2011
The aim of this paper is to investigate the problem of the *-ideal retraction of some special abundant semigroups. In order to get a characterization for an abundant semigroup satisfying the regularity condition to have the *-ideal property, we first give the definition of the *-ideal retraction property and consider in the condition of a semigroup S with a zero element 0 such that each *- ideal of S has a dual, S has the *-retraction property. Based on the regularity condition and idempotent method, we give a necessary and sufficient condition for an abundant semigroup satisfying the regularity condition to have the *-ideal property. Finally, an example is given to establish a characterizations of adequate semigroups satisfying the regularity condition with the *-ideal retraction property.