Linkage property under the amalgamated construction

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.

Keywords:

• Amalgamated algebra
• Cohen-Macaulay ring
• idealization
• linkage

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 13A15
• 13H10
• 14M06

Acknowledgment

The author is grateful to the referee for his/her careful reading of the paper and valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was in part supported by a grant from IPM (No.991300116).