# Notes on amalgamated duplication of a ring along an ideal

Document Type: Research Paper

Authors

Department of Mathematics, University of Tabriz

Abstract

In this paper, we study some ring theoretic properties of the
amalgamated duplication ring $R\bowtie I$ of a commutative
Noetherian ring $R$ along an ideal $I$ of $R$ which was introduced by
D'Anna and Fontana. Indeed, it is determined that when $R\bowtie I$
satisfies Serre's conditions $(R_n)$ and $(S_n)$, and when is a
normal ring, a generalized Cohen-Macaulay ring and finally a filter
ring.

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Main Subjects

### History

• Receive Date: 16 November 2013
• Revise Date: 14 April 2014
• Accept Date: 19 April 2014