SOME NEW CHARACTERIZATIONS OF QUASI-FROBENIUS RINGS BY USING PURE-INJECTIVITY
Bull. Korean Math. Soc.
Published online September 10, 2019
Ali Moradzadeh-Dehkordi
UNIVERSITY OF SHAHREZA, SHAHREZA, IRAN
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 : 16L60, 13C11; Secondary: 16P40
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