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

References

1.

H. Ananthnarayan, L. Avramov, and W. Frank Moore, Connected sums of Gorenstein local rings, arXiv: 1005.1304v2 [math.AC] 10 Feb 2011.

2.

3.

Y. Aoyama and S. Goto, On the endomorphism ring of the canonical module, J. Math. Kyoto Univ. 25 (1985), no. 1, 21-30.

4.

A. Bagheri, M. Salimi, E. Tavasoli, and S. Yassemi, A construction of quasi-Gorenstein rings, J. Algebra Appl, to appear.

5.

W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge University press, Cambridge, 1993.

7.

M. D'Anna, C. A. Finocchiaro, and M. Fontana, Amalgamated algebras along an ideal, Commutative algebra and its applications, 155-172, Walter de Gruyter, Berlin, 2009.

8.

M. D'Anna and M. Fontana, An amalgamated duplication of a ring along an ideal, J. Algebra Appl. 6 (2007), no. 3, 443-459.

10.

M. Hochster, Cyclic purity versus purity in excellent Noetherian ringss, Trans. Amer. Math. Soc. 231 (1977), no. 2, 463-488.

11.

H. Matsumura, Commutative Ring Theory, second ed., Studies in Advanced Mathemetics, vol.8, University Press, Cambridge, 1989.

12.

E. Platte and U. Storch, Invariante regulare Differential-formen auf Gorenstein-Algebren, Math. Z. 157 (1997), no. 1, 1-11.

13.

M. R. Pournaki, M . Tousi, and S. Yassemi, Tensor products of approximately Cohen-Macaulay rings, Comm. Algebra 34 (2006), no. 8, 2857-2866.

14.

S. Yassemi, On at and injective dimension, Ital. J. Pure Appl. Math. No. 6 (1999), 33-41.