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.
Acknowledgments
I would like to thank the anonymous referee for his/her thorough review and useful comments that helped improve the clarity and the relevance of this paper. Also I am very grateful to Professor Noômen Jarboui for his many helpful suggestions and comments.