Abstract

Let R and S be commutative rings with identity, $f:R\to S$ a ring homomorphism and J an ideal of S. Then, the subring $R{\bowtie }^{f}J:=\{(a,f(a)+j)|a\in R$ and $j\in J\}$ of R × S is called the amalgamation of R with S along J with respect to f. In this article, we investigate when two extended ideals in $R{\bowtie }^{f}J$ of R are linked.

中文翻译：

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合并建设下的联动财产

摘要

令R和S是具有身份的交换环，$F：\mathrm{电阻}\to 秒$一个环同态，J是S的理想。然后，子环$\mathrm{电阻}{\bowtie }^{F}J：=\{(\mathrm{一种},F(\mathrm{一种})+j)|\mathrm{一种}\in \mathrm{电阻}$ 和 $j\in J\}$的- [R  × 小号被称为的合并- [R与小号沿Ĵ相对于˚F。在本文中，我们研究了当两个扩展理想在$\mathrm{电阻}{\bowtie }^{F}J$的[R被连接。