Abstract
IFP-injective modules act in ways similar to injective modules. In this paper, we first investigate the existence of IFP-injective covers. It is shown that over any ring R, IFP-injective cover always exists. Secondly, we prove that S −1 M is an IFP-injective S −1 R-module for any IFP-injective R-module M over any ring R.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Bican, R. El Bashir and E. E. Enochs, All modules have flat covers, Bull. London Math. Soc., 33 (2001), 385–390.
R. R. Colby, Rings which have flat injective modules, J. Algebra, 35 (1975), 239–252.
E. C. Dade, Localization of injective modules, Journal of Algebm, 69 (1981), 416–425.
E. E. Enochs, A note on absolutely pure modules, Canad. Math. Bull., 19 (1976), 361–362.
E. E. Enochs, Injective and flat covers, envelopes and resolvents, Ismel J. Math., 39 (1981), 189–209.
E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, Berlin-New York: Walter de Gruyter, (2000).
E. E. Enochs and O. M. G. Jenda, Copure injective resolutions, flat resolutions and dimensions, Comment. Math. Univ. Carolin, 34 (1993), 203–211.
B. Lu and Z. K. Lin, IFP-flat modules and JFP-injective modules, Common. Algebm, 40 (2012), 361–374.
K. R. Pinzon, Absolutely Pure Modules, Ph.D thesis, University of Kentucky, (2005).
K. Pinzon, Absolutely Pure Covers, Comm. Algebra, 36 (2008), 2186–2194.
J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, (1979).
B. Stenstro, Coherent rings and FP-injective modules, J. London Math. Soc., 2 (1970), 323–329.
J. Xu, Flat Covers of Modules, Lecture Notes in Math., 1634. Berlin-Heidelberg-New York: Springer-Verlag, (1996).
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by National Natural Science Foundation of China (No.11201376, 11261050).
Rights and permissions
About this article
Cite this article
Lu, B., Liu, Z. IFP-injective, IFP-flat modules and localizations. Indian J Pure Appl Math 45, 837–849 (2014). https://doi.org/10.1007/s13226-014-0092-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-014-0092-5