The amalgamated duplication of a ring along a semidualizing ideal

Maryam Salimi; Elham Tavasoli; Siamak Yassemi

Rendiconti del Seminario Matematico della Università di Padova (2013)

  • Volume: 129, page 115-128
  • ISSN: 0041-8994

How to cite

top

Salimi, Maryam, Tavasoli, Elham, and Yassemi, Siamak. "The amalgamated duplication of a ring along a semidualizing ideal." Rendiconti del Seminario Matematico della Università di Padova 129 (2013): 115-128. <http://eudml.org/doc/275128>.

@article{Salimi2013,
author = {Salimi, Maryam, Tavasoli, Elham, Yassemi, Siamak},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {amalgamated duplication; semidualizing; totally reflexive; Gorenstein projective},
language = {eng},
pages = {115-128},
publisher = {Seminario Matematico of the University of Padua},
title = {The amalgamated duplication of a ring along a semidualizing ideal},
url = {http://eudml.org/doc/275128},
volume = {129},
year = {2013},
}

TY - JOUR
AU - Salimi, Maryam
AU - Tavasoli, Elham
AU - Yassemi, Siamak
TI - The amalgamated duplication of a ring along a semidualizing ideal
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2013
PB - Seminario Matematico of the University of Padua
VL - 129
SP - 115
EP - 128
LA - eng
KW - amalgamated duplication; semidualizing; totally reflexive; Gorenstein projective
UR - http://eudml.org/doc/275128
ER -

References

top
  1. [1] A. Bagheri - M. Salimi - E. Tavasoli - S. Yassemi, A Construction of Quasi-Gorenstein Rings, J. Algebra Appl. 11, no. 1 (2012), 1250013 (9 pages). Zbl1245.13017MR2900883
  2. [2] W. Bruns - J. Herzog, Cohen-Macaulay Rings, Cambridge University press, Cambridge, 1993. MR1251956
  3. [3] L. W. Christensen, Gorenstein Dimensions, Lecture Notes in Math. Vol. 1747, Springer, Berlin, 2000. Zbl0965.13010MR1799866
  4. [4] L. W. Christensen - H. B. Foxby - H. Holm, Beyond Totally Reflexive Modules and Back: a survey on Gorenstein dimensions, ]Commutative Algebra-Noetherian and non-Noetherian Perspectives^, 101-143, Springer, New York, 2011. Zbl1225.13019MR2762509
  5. [5] M. D'Anna, A construction of Gorenstein rings, J. Algebra306 (2006), pp. 507–519. Zbl1120.13022MR2271349
  6. [6] M. D'Anna - M. Fontana, An amalgamated duplication of a ring along an ideal, J. Algebra Appl. 6, no. 3 (2007), pp. 443–459. Zbl1126.13002MR2337762
  7. [7] E. E. Enochs - O. M. G. Jenda, Relative Homological Algebra, de Gruyter Expositions in Mathematics, vol. 30, Walter de Gruyter and Co., Berlin, 2000. MR1753146
  8. [8] N. Epstein - Y. Yao, Criteria for Flatness and Injectivity, Math. Z. 271, no. 3-4 (2012), pp. 1193–1210. Zbl1245.13009MR2945604
  9. [9] H. B. Foxby, Gorenstein Modules and Related Modules, Math. Scand. 31, (1972), pp. 267–284. Zbl0272.13009MR327752
  10. [10] E. S. Golod, G-dimension and Generalized Perfect Ideals, Trudy Mat. Inst. Steklov. 165, (1984), pp. 62–66. MR752933
  11. [11] H. Holm - P. Jørgensen, Cohen-Macaulay Homological Dimensions, Rend. Semin. Mat. Univ. Padova, 117 (2007), pp. 87–112. Zbl1150.13001MR2351787
  12. [12] M. Chhiti - N. Mahdou, Homological dimension of the amalgamated duplication of a ring along a pure ideal, Afr. Diaspora J. Math. (N. S.) 10, no. 1, (2010), pp. 1–6. Zbl1238.13022MR2591686
  13. [13] N. Mahdou - M. Tamekkante, Gorenstein global dimension of an amalgamated duplication of a coherent ring along an ideal, Mediterr. J. Math. 8, no. 3 (2011), pp. 293–305. Zbl1229.18013MR2824582
  14. [14] M. Nagata, Local Rings , Interscience, New York, 1962. MR155856
  15. [15] S. Sather-Wagstaff, Semidualizing modules, URL:http://www.ndsu.edu/pubweb/~ssatherw/. Zbl1127.13007
  16. [16] J. Shapiro, On a construction of Gorenstein rings proposed by M. D'Anna, J. Algebra, 323 (2010), pp. 1155–1158. Zbl1184.13069MR2578598
  17. [17] E. Tavasoli - M. Salimi - A. Tehranian, Amalgamated duplication of some special rings, Bulletin of Korean Math. Soc. 49 no. 5 (2012) pp. 989–996. Zbl1255.13015MR3012966
  18. [18] W. V. Vasconcelos, Divisor Theory in Module Categories, North-Holland Math. Stud., vol. 14, North-Holland Publishing Co., Amsterdam, (1974). Zbl0296.13005MR498530
  19. [19] T. Wakamatsu, On modules with trivial self-extensions, J. Algebra, 114, no. 1 (1988), pp. 106–114. Zbl0646.16025MR931903
  20. [20] S. Yassemi, On flat and injective dimension, Italian Journal of Pure and Applied Mathematics, N. 6 (1999), pp. 33–41. Zbl0964.16007MR1758529

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.