On relative Baer property and relative t-Baer property of modules

In this paper, the notions of relative Baer and relative [Formula: see text]-Baer modules are used to obtain characterizations of Baer modules and [Formula: see text]-Baer modules. It is also proved that for [Formula: see text]-modules [Formula: see text] such that [Formula: see text] is [Formula: see text]-injective for all [Formula: see text] and for an [Formula: see text]-module [Formula: see text], the finite direct sum of [Formula: see text] is [Formula: see text]-Baer (respectively, [Formula: see text]-[Formula: see text]-Baer) if and only if [Formula: see text] is [Formula: see text]-Baer (respectively, [Formula: see text]-[Formula: see text]-Baer) for all [Formula: see text]. We provide examples which illustrate our results.