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AMALGAMATED DUPLICATION OF SOME SPECIAL RINGS

  • Tavasoli, Elham (Department of Mathematics Science and Research Branch Islamic Azad University) ;
  • Salimi, Maryam (Department of Mathematics Science and Research Branch Islamic Azad University) ;
  • Tehranian, Abolfazl (Department of Mathematics Science and Research Branch Islamic Azad University)
  • Received : 2011.05.18
  • Published : 2012.09.30

Abstract

Let R be a commutative Noetherian ring and let I be an ideal of R. In this paper we study the amalgamated duplication ring $R{\bowtie}I$ which is introduced by D'Anna and Fontana. It is shown that if R is generically Cohen-Macaulay (resp. generically Gorenstein) and I is generically maximal Cohen-Macaulay (resp. generically canonical module), then $R{\bowtie}I$ is generically Cohen-Macaulay (resp. generically Gorenstein). We also de ned generically quasi-Gorenstein ring and we investigate when $R{\bowtie}I$ is generically quasi-Gorenstein. In addition, it is shown that $R{\bowtie}I$ is approximately Cohen-Macaulay if and only if R is approximately Cohen-Macaulay, provided some special conditions. Finally it is shown that if R is approximately Gorenstein, then $R{\bowtie}I$ is approximately Gorenstein.

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