\((m, n)\)-closed \(\delta \)-primary ideals in amalgamation
Let \(R\) be a commutative ring with \(1\neq 0\). Let \(Id(R)\) be the set of all ideals of \(R\) and let \(\delta: Id(R)\longrightarrow Id(R)\) be a function. Then \(\delta\) is called an expansion function of the ideals of \(R\) if whenever \(L, I, J\) are ideals of \(R\) with \(J\subseteq I,\) then \(L\subseteq \delta(L)\) and \(\delta(J)\subseteq \delta(I)\). Let \(\delta\) be an expansion function of the ideals of \(R\) and \(m\geq n \ge 0\) be positive integers. Then a proper ideal \(I\) of \(R\) is called an \((m,n)\)-closed \(\delta\)-primary ideal (resp., weakly \((m,n)\)-closed \(\delta\)-primary ideal) if \(a^m \in I\) for some \(a\in R\) implies \(a^n\in \delta(I)\) (resp., if \(0\neq a^m\in I\) for some \(a\in R\) implies \(a^n \in \delta(I))\). Let \(f: A\longrightarrow B\) be a ring homomorphism and let \(J\) be an ideal of \(B\). This paper investigates the concept of \((m, n)\)-closed \(\delta\)-primary ideals in the amalgamation of \(A\) with \(B\) along \(J\) with respect to \(f\).
\((m, n)\)-closed \(\delta \)-primary ideal
weakly \((m, n)\)-closed \(\delta \)-primary ideal
scientific article; zbMATH DE number 7924502
scientific article