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SOME NEW CHARACTERIZATIONS OF QUASI-FROBENIUS RINGS BY USING PURE-INJECTIVITY
Moradzadeh-Dehkordi, Ali Korean Mathematical Society 2020 대한수학회보 Vol.57 No.2
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.
Some new characterizations of quasi-Frobenius rings by using pure-injectivity
Ali Moradzadeh-Dehkordi 대한수학회 2020 대한수학회보 Vol.57 No.2
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.