Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 1, Issue 1, August 2017, pp 30-41

FFI-injective and FFI-flat modules

A. Umamaheswaran

Department of Mathematics, Periyar University, Salem - 636 011, TN, India.


In this paper we introduce FFI-projective, FFI-injective and FFI-flat modules and give a characterization of FFI-injective modules and FFI-projective modules. When all left R-modules has FI-injective covers, we show that a left R-module is FFI-injective if and only if M is a direct sum of an injective left Rmodule and a reduced FFI-injective left R-module. Class of all FFI-injective left R-modules is closed under direct limits whenever all modules has FFI-injective cover. Furthermore, we show that class of all FFI-projective modules is closed under inverse limits whenever every left R-module has an epic FFI-projective envelope.


FFI-injective module, FFI-flat module, FFI-projective module,(Pre)envelope, (Pre)cover.

Subject classification: 16D10, 16D40, 16E30.



1. E.E. Enochs, injective and flat covers, envelopes and resolvents, Isrel J. Math. 39 (1981)189-209.

2. E.E.Enochs and O.M.G. Jenda, Relative Homological Algebra, de Gruyter Exp. Math., Vol.30, Walter de Gruyter: Berlin-New York, 2000.

3. L Fuchs and L Salce. Modules over Non-Noetherian Domains, Mathematical Surveys andMonographs, American Mathematical Society, Providence, Volume 84, 2001.

4. L. Mao, N.Q. Ding, F I-injective and F I-flat modules, Journal of Algebra, 309, 367-385, 2007.

5. B. Stenstr¨om, Coherent Rings and F P-injective modules, J. London Math. Soc., 2 (1970),323-329.

6. J. Xu, Flat covers of Modules, Lecture Notes in Mathematics. Vol 1634 Springer-Verlag,Germany, 1996.

mail to for access the full article

Visitors count