Bulletin of the
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BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2020; 57(2): 371-381

Online first article September 10, 2019      Printed March 31, 2020

https://doi.org/10.4134/BKMS.b190247

Copyright © The Korean Mathematical Society.

Some new characterizations of quasi-Frobenius rings by using pure-injectivity

Ali Moradzadeh-Dehkordi

Institute for Research in Fundamental Sciences (IPM)

Abstract

A ring $R$ is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L.~Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if $R$ is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.

Keywords: Right pure-injective ring, right Artinian ring, quasi-Frobenius ring

MSC numbers: Primary 16L60, 13C11; Secondary 16P40

Supported by: This research was in part supported by a grant from IPM (No. 98160419).

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