Semigroup compactifications in terms of filters

We present a study of semigroup compactifications of a semitopological semigroup $S$ using certain filters on $S$. We characterize closed subsemigroups and closed left, right, and two-sided ideals in any semigroup compactification of any semitopological semigroup $S$ in terms of these filters and in terms of ideals of the corresponding $m$-admissible subalgebra of $C(S)$. Furthermore, we characterize those points in any semigroup compactification of $S$ which belong either to the smallest ideal of the semigroup compactification or to the closure of this smallest ideal.