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