Some new characterizations of quasi-Frobenius rings by using pure-injectivity
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 371-381
https://doi.org/10.4134/BKMS.b190247
Published online September 10, 2019
Printed March 31, 2020
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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