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Paper   IPM / M / 15833
School of Mathematics
  Title:   Some new characterizations of quasi-Frobenius rings by using pure-injectivity
  Author(s):  Ali Moradzadeh-Dehkordi
  Status:   Published
  Journal: Bull. Korean Math. Soc.
  Vol.:  57
  Year:  2020
  Pages:   371-381
  Supported by:  IPM
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.

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