Abstract
Let R be a commutative ring with identity and a multiplicative subset. We define a proper ideal P of R disjoint from S to be S-primary if there exists an such that for all if then or We show that S-primary ideals enjoy analogs of many properties of primary ideals and we study the form of S-primary ideals of the amalgamation of A with B along an ideal J with respect to f (denoted by ), introduced and studied by D’Anna et al. S-primary ideals of the form of the trivial ring extensions and S-primary ideals of the form and of the bi-amalgamations are characterized.
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