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http://dx.doi.org/10.4134/BKMS.2012.49.5.989

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 989-996 More about this Journal
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.
Keywords
amalgamated duplication; generically Cohen-Macaulay; generically Gorenstein; approximately Cohen-Macaulay; approximately Gorenstein;
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