Some further results on II-γ and II-γkγk-covers

In this paper we primarily consider the notion of I-γI-γ-covers recently introduced in [11] as well as related notion of I-γkI-γk-covers [9] and make some further investigations. In particular we consider the notion of κ-covers studied by Di Maio, Kočinac, Meccariello and Caserta in [8] and [18], and establish some results involving I-γI-γ-covers (I-γkI-γk-covers) and κ-covers. Our results extend the earlier results proved in [6], [8], [18] and [29] and present a more general version using the notion of ideals.