# Complexes of $C$-projective modules

Document Type : Research Paper

Authors

1 Faculty of Mathematical Sciences and Computer‎, ‎Kharazmi University‎, ‎Tehran‎, ‎Iran‎.

2 Faculty of Mathematical Sciences and Computer‎, ‎Kharazmi University‎, ‎Tehran‎, ‎Iran and School of Mathematics‎, ‎Institute for Research in Fundamental Sciences (IPM)‎, ‎P.O‎. ‎Box‎ ‎19395-5746‎, ‎Tehran‎, ‎Iran.

Abstract

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular. It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.

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Main Subjects

#### References

E. Amanzadeh and M. T. Dibaei, Auslander class, GC and C--projective modules modulo exact zero-divisors, Comm. Algebra 43 (2015), no. 10, 4320--4333.
L. L. Avramov and A. Martsinkovsky, Absolute, relative, and Tate cohomology of modules of inite Gorenstein dimension, Proc. London Math. Soc. (3) 85 (2002), no. 2, 393--440.
R-O. Buchweitz and H. Flenner, Strong global dimension of commutative rings and schemes, J. Algebra 422 (2015) 741--751.
L. W. Christensen and H. B. Foxby, Hyperhomological algebra with applications to commutative rings,  http://www.math.ttu.edu/~lchriste/download/918-final.pdf
M. T. Dibaei and M. Gheibi, Sequence of exact zero--divizors, arXiv:1112.2353v3 (2012).
E. E. Enochs and O. M. G. Jenda, Relative homological algebra, 30, Walter de Gruyter & Co., Berlin, 2000.
S. I. Gelfand and Y. I. Manin, Methods of Homological Algebra, Springer-Verlag, Berlin, 1996.
H. Holm and P. Jørgensen, Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl. Algebra 205 (2006), no. 2, 423--445.
H. Holm and D. White, Foxby equivalence over associative rings, J. Math. Kyoto Univ. 47 (2007), no. 4, 781--808.
J. J. Rotman, An Introduction to Homological Algebra, Springer Universitext, Second Edition, New York, 2009.
S. Sather-Wagstaff, Semidualizing modules, http://www.ndsu.edu/pubweb/~ssatherw/DOCS/sdm.pdf
S. Sather-Wagstaff, T. Sharif and D. White, Stability of Gorenstein categories, J. Lond. Math. Soc. (2) 77 (2008), no. 2, 481--502.
R. Takahashi and D. White, Homological aspects of semidualizing modules, Math. Scand. 106 (2010), no. 1, 5--22.
D. White, Gorenstein projective dimension with respect to a semidualizing module, J. Commut. Algebra 2 (2010), no. 1, 111--137.

### History

• Receive Date: 13 March 2015
• Revise Date: 08 June 2015
• Accept Date: 17 June 2015
• First Publish Date: 01 August 2016