Quasi-S-primary ideals of commutative rings

Abstract

Let R be a commutative ring with 1 not equal 0 and S be a multiplicatively closed subset of R. We call an ideal I of R disjoint with S quasi-S-primary if there exists an s is an element of S such that whenever a, b is an element of R and ab is an element of I, then sa is an element of root l or sb is an element of root l. We investigate many properties and characterizations of quasi-S-primary ideals. We discuss the form of quasi-S-primary ideals in polynomial, power series, the Serre's conjecture and the Nagata rings. Futhermore, we study quasi-S-primary ideals in amalgamated algebras. Our results allow us to construct original examples of quasi-S-primary ideals.