[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j160014

RINGS OF COPURE PROJECTIVE DIMENSION ONE

Xiong, Tao (Department of Mathematics Sichuan Normal University)

Publication Information

Journal of the Korean Mathematical Society / v.54, no.2, 2017 , pp. 427-440 More about this Journal

Abstract

In this paper, in terms of the notions of strongly copure projective modules and the copure projective dimension cpD(R) of a ring R were defined in [12], we show that a domain R has $cpD(R){\leq}1$ if and only if R is a Gorenstein Dedekind domain.

Keywords

strongly copure projective modules; copure projective dimension; Gorenstein Dedekind domains;

Citations & Related Records

Reference

1	J. Abuhlail and M. Jarrar, Tilting modules over almost perfect domains, J. Pure Appl. Algebra 215 (2011), no. 8, 2024-2033. DOI
2	H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. DOI
3	D. Bennis, A short survey on Gorenstein global dimension, Actes des rencontres du C.I.R.M. 2 (2010), no. 2, 115-117. DOI
4	R. R. Colby, Rings which have flat injective modules, J. Algebra 35 (1975), 239-252. DOI
5	T. J. Cheatham and D. R. Stone, Flat and projective character modules, Proc. Amer. Math. Soc. 81 (1981), no. 2, 175-177. DOI
6	N. Q. Ding and J. L. Chen, The flat dimensions of injective modules, Manuscripta Mathematica 78 (1993), no. 2, 165-177. DOI
7	N. Q. Ding and J. L. Chen, On copure flat modules and flat resolvents, Comm. Algebra 24 (1996), no. 3, 1071-1081. DOI
8	E. E. Enochs and O. M. G. Jenda, Copure injective resolutions, flat resolvents and dimensions, Comment. Math. Univ. Carolin. 34 (1993), no. 2, 203-211.
9	E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, Walter de Gruyter, Berlin-New York 2000.
10	D. J. Fieldhouse, Character modules, dimension and purity, GlasgowMath. J. 13 (1972), 144-146.
11	X. H. Fu and N. Q. Ding, On strongly copure flat modules and copure flat dimensions, Comm. Algebra 38 (2010), no. 12, 4531-4544. DOI
12	X. H. Fu and H. Y. Zhu, and N. Q. Ding, On copure projective modules and copure projective dimensions, Comm. Algebra 40 (2012), no. 1, 343-359. DOI
13	Z. H. Gao, n-copure projective modules, Mathematical Notes 97 (2015), no. 1, 50-56. DOI
14	R. Gobel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules, Berlin-New York: Walter de Gruyter, 2006.
15	K. Hu and F. G. Wang, Some results on Gorenstein Dedekind domains and their factor rings, Comm. Algebra 41 (2013), no. 1, 284-293. DOI
16	S. Jain, Flat and FP-injective, Proc. AMS. 41 (1979), 437-442.
17	C. U. Jensen, On the vanishing of ${\lim_{\leftarrow}^{(i)}}$ , J. Algebra 15 (1970), 155-166.
18	J. J. Rotman, An Introduction to Homological Algebra, 2nd ed. New York: Springer Science+Business Media, LLC, 2009.
19	M. Raynaud and L. Gruson, Griteres de plattitude et de projectivite. Techniques de "platification" d'un module, Invent. Math. 13 (1971), 1-89. DOI
20	J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York 1979.
21	L. Salce, Almost perfect domains and their modules, In Commutative algebra: Noetherian and non-Noetherian perspectives, pp. 363-386, New York, Springer, 2011.
22	B. Stenstrom, Coherent rings and FP-injective modules, J. London Math. Soc. 2 (1970), 323-329.
23	T. Xiong, F. G. Wang, and K. Hu, Copure Projective Modules and CPH-rings, J. Sichuan Normal University (Natural Science) 36 (2013), no. 2, 198-201.