AMALGAMATED DUPLICATION OF SOME SPECIAL RINGS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 49, Issue 5, 2012, pp.989-996
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2012.49.5.989

Title & Authors

AMALGAMATED DUPLICATION OF SOME SPECIAL RINGS

Tavasoli, Elham; Salimi, Maryam; Tehranian, Abolfazl;

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 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 is generically Cohen-Macaulay (resp. generically Gorenstein). We also de ned generically quasi-Gorenstein ring and we investigate when is generically quasi-Gorenstein. In addition, it is shown that 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 is approximately Gorenstein.

Keywords

amalgamated duplication;generically Cohen-Macaulay;generically Gorenstein;approximately Cohen-Macaulay;approximately Gorenstein;

Language

English

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