Yıl 2010, Cilt 8, Sayı 8, Sayfalar 140 - 152 2010-12-01

WEAK GORENSTEIN GLOBAL DIMENSION

Driss Bennis [1]

102 161

In this paper, we investigate the weak Gorenstein global dimension. We are mainly interested in studying the problem when the left and right weak Gorenstein global dimensions coincide. We first show, for GFclosed rings, that the left and right weak Gorenstein global dimensions are equal when they are finite. Then, we prove that the same equality holds for any two-sided coherent ring. We conclude with some examples and a brief discussion of the scope and limits of our results.
Gorenstein flat dimension, weak Gorenstein global dimension, weak global dimension, GF-closed rings
  • D. Bennis, Rings over which the class of Gorenstein flat modules is closed under extensions, Comm. Algebra, 37 (2009), 855–868.
  • D. Bennis, A Note on Gorenstein Flat Dimension. Accepted for Publication in Algebra Coll. Available from arXiv:0811.2650v1.
  • D. Bennis and N. Mahdou, Global Gorenstein Dimensions, Proc. Amer. Math. Soc., 138 (2010), 461–465.
  • L. Bican, R. El Bashir and E. Enochs, All modules have flat covers, Bull. London Math. Soc., 33 (2001), 385–390.
  • N. Bourbaki, Alg`ebre Homologique, Chapitre 10, Masson, Paris, 1980.
  • T. J. Cheatham and D. R. Stone, Flat and projective character modules, Proc. Amer. Math. Soc., 81 (1981), 175–177.
  • J. Chen and N. Ding, Coherent rings with finite self-FP-injective dimension, Comm. Algebra, 24 (1996), 2963–2980.
  • L. W. Christensen, Gorenstein Dimensions, Lecture Notes in Math., Springer- Verlag, Berlin, 2000.
  • L. W. Christensen, A. Frankild and H. Holm, On Gorenstein projective, injec- tive and flat dimensions - a functorial description with applications, J. Algebra, (2006), 231–279.
  • R. R. Colby, On Rings which have flat injective modules, J. Algebra, 35 (1975), –252.
  • E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, de Gruyter Expositions in Mathematics, Walter de Gruyter & Co., Berlin, 2000.
  • E. E. Enochs and O. M. G. Jenda, Torrecillas, B. Gorenstein flat modules, Nanjing Daxue Xuebao Shuxue Bannian Kan, 10 (1993), 1–9.
  • H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra, 189 (2004), 167–193.
  • H. Holm, Rings with finite Gorenstein injective dimension, Proc. Amer. Math. Soc., 132 (2004), 1279–1283.
  • B. Madox, Absolutely pure modules. Proc. Amer. Math. Soc., 18 (1967), 155–
  • J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.
  • B. Stenstr¨om, Coherent rings and FP-injective modules, J. London Math. Soc., (1970), 323–329.
  • J. Xu, Flat Covers of Modules, Lecture Notes in Math., Springer-Verlag, Berlin, Driss Bennis Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202,
  • University S. M. Ben Abdellah Fez, Morocco, e-mail: driss bennis@hotmail.com
Konular
Diğer ID JA33HK82BT
Dergi Bölümü Makaleler
Yazarlar

Yazar: Driss Bennis

Bibtex @ { ieja266435, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2010}, volume = {8}, pages = {140 - 152}, doi = {}, title = {WEAK GORENSTEIN GLOBAL DIMENSION}, key = {cite}, author = {Bennis, Driss} }
APA Bennis, D . (2010). WEAK GORENSTEIN GLOBAL DIMENSION. International Electronic Journal of Algebra, 8 (8), 140-152. Retrieved from http://dergipark.gov.tr/ieja/issue/25212/266435
MLA Bennis, D . "WEAK GORENSTEIN GLOBAL DIMENSION". International Electronic Journal of Algebra 8 (2010): 140-152 <http://dergipark.gov.tr/ieja/issue/25212/266435>
Chicago Bennis, D . "WEAK GORENSTEIN GLOBAL DIMENSION". International Electronic Journal of Algebra 8 (2010): 140-152
RIS TY - JOUR T1 - WEAK GORENSTEIN GLOBAL DIMENSION AU - Driss Bennis Y1 - 2010 PY - 2010 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 140 EP - 152 VL - 8 IS - 8 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2019 ER -
EndNote %0 International Electronic Journal of Algebra WEAK GORENSTEIN GLOBAL DIMENSION %A Driss Bennis %T WEAK GORENSTEIN GLOBAL DIMENSION %D 2010 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 8 %N 8 %R %U
ISNAD Bennis, Driss . "WEAK GORENSTEIN GLOBAL DIMENSION". International Electronic Journal of Algebra 8 / 8 (Aralık 2010): 140-152.