AMALGAMATED DUPLICATION OF SOME SPECIAL RINGS

Title & Authors
AMALGAMATED DUPLICATION OF SOME SPECIAL RINGS
Tavasoli, Elham; Salimi, Maryam; Tehranian, Abolfazl;

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 $\small{R{\bowtie}I}$ 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 $\small{R{\bowtie}I}$ is generically Cohen-Macaulay (resp. generically Gorenstein). We also de ned generically quasi-Gorenstein ring and we investigate when $\small{R{\bowtie}I}$ is generically quasi-Gorenstein. In addition, it is shown that $\small{R{\bowtie}I}$ 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 $\small{R{\bowtie}I}$ is approximately Gorenstein.
Keywords
amalgamated duplication;generically Cohen-Macaulay;generically Gorenstein;approximately Cohen-Macaulay;approximately Gorenstein;
Language
English
Cited by
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