Strongly S-1-absorbing primary ideals of commutative rings

Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be a multiplicative closed subset of [Formula: see text]. In this paper, we introduce and study the concept of strongly [Formula: see text]-1-absorbing primary ideals as subclass of primary ideals. We define a proper ideal [Formula: see text] disjoint with [Formula: see text] to be a strongly [Formula: see text]-1-absorbing primary ideal if there exists an [Formula: see text] such that for all nonunit elements [Formula: see text] and [Formula: see text], we have [Formula: see text] or [Formula: see text]. We characterize local rings and UN-rings with the help of strongly [Formula: see text]-1-absorbing primary ideals. Furthermore, we investigate the transfer of the above properties to trivial ring extensions, amalgamations and bi-amalgamations of rings along an ideal.