Research ArticleNo Access

On Nagata rings with amalgamation properties

Ali Molkhasi

Institute of Mathematics, Farhangian University, Tabriz, Iran

E-mail Address: molkhasi@gmail.com

Corresponding author.

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and

Kar Ping Shum

School of Mathematics and Statistics, Southwest University, Beinai, Chongqing, P. R. China

E-mail Address: kpshum@swu.edu.cn

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https://doi.org/10.1142/S1793557121501369Cited by:0 (Source: Crossref)

Abstract

Let $R$ $R$ and $S$ $S$ be two commutative rings with unity, let $J$ $J$ be an ideal of $S$ $S$ and $φ : R \to S$ $φ : R \to S$ be a ring homomorphism. In this paper, we give a characterization for the amalgamated algebra $R ⋈^{φ} J$ $R ⋈^{φ} J$ to be a Nagata ring, a strong S-domain, and a catenarian. Also, we investigate the conditions that the ring of Hurwitz series over $R ⋈^{φ} J$ $R ⋈^{φ} J$ has a complete comaximal factorization.

Communicated by S. H. Ng

Keywords:

AMSC: 13A15, 13D05

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