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http://dx.doi.org/10.4134/BKMS.b190247

SOME NEW CHARACTERIZATIONS OF QUASI-FROBENIUS RINGS BY USING PURE-INJECTIVITY  

Moradzadeh-Dehkordi, Ali (Faculty of Basic Sciences University of Shahreza)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 371-381 More about this Journal
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;
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