IJPAM: Volume 113, No. 2 (2017)

Title

SELF FP-INJECTIVE AMALGAMATED DUPLICATION
OF A RING ALONG AN IDEAL

Authors

Mohammed Tamekkante$^1$, El Mehdi Bouba$^2$, Khalid Louartiti$^{3}$
$^{1,2}$Faculty of Science
Moulay Ismail University
Box 11201, Zitoune, Meknes, MOROCCO
$^3$Faculty of Science
University Hassan II
Ben M'SIK, Box 7955, Sidi Othmam, Casablanca, MOROCCO

Abstract

Let $R$ be commutative ring and let $I$ be an ideal of $R$. The amalgamated duplication of $R$ along $I$ is subring of $R \times R$ given by $R\bowtie I=\{ (r,r+i)/ r \in R, i\in I\}$. In this paper, we characterize the amalgamated duplication of a ring along an ideal to be self $\FP$-injective provided $I$ is finitely generated. Hence, we deduce a characterization of this construction to be $\IF$-ring, and to be quasi-Frobenius ring.

History

Received: October 11, 2016
Revised: December 28, 2016
Published: March 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 13D05, 13D07
Key Words and Phrases: amalgamated duplication of a ring along an ideal, FP-injective dimension.

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How to Cite?

DOI: 10.12732/ijpam.v113i2.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 2
Pages: 235 - 240


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