REFERENCES
- Al-Kawarit , W. , Couchot , F. ( 2011 ). Comparison of some purities, flatnesses and injectivities . Comm. Algebra 39 : 3879 – 3896 .
- Anderson , F. W. , Fuller , K. R. ( 1992 ). Rings and Categories of Modules. , 2nd ed. Grad. Texts in Math. , Vol. 13 . Berlin : Springer-Verlag .
- Azumaya , G. ( 1992 ). Countabled Generatedness Version of Rings of Pure Global Dimension 0 . Representations of Algebra , Cambridge University Press .
- Behboodi , M. , Ghorbani , A. , Moradzadeh-Dehkordi , A. , Shojaee , S. H. On left Köthe rings and a generalization of a Köthe-Cohen-Kaplansky theorem . Proc. Amer. Math. Soc. (to appear) .
- Chase , S. U. ( 1960 ). Direct products of modules . Trans. Amer. Math. Soc. 97 : 457 – 473 .
- Cohen , I. S. , Kaplansky , I. ( 1951 ). Rings for which every module is a direct sum of cyclic modules . Math. Z. 54 : 97 – 101 .
- Couchot , F. ( 2006 ). RD-flatness and RD-injectivity . Comm. Algebra 34 : 3675 – 3689 .
- Crawley-Boevey , W. ( 1994 ). Locally finitely presented additive categories . Comm. Algebra 22 : 1641 – 1674 .
- Crivei , I. , Crivei , S. ( 2006 ). (m, n)-purity for modules . Bull. Math. Soc. Sc. Math. Roumanie Tome 49 ( 97 ): 37 – 46 .
- Damiano , R. F. ( 1979 ). Coflat rings and modules . Pacific J. Math. 81 : 349 – 369 .
- Dauns , J. ( 1994 ). Modules and Rings . Cambridge : Cambridge University Press .
- Divaani-Azar , K. , Esmkhani , M. A. , Tousi , M. ( 2006 ). Some criteria of cyclically pure injective modules . J. Algebra 304 ( 1 ): 367 – 381 .
- Facchini , A. ( 1987 ). Relative injective and pure-injective modules over Prüfer rings . J. Algebra 110 : 380 – 406 .
- Facchini , A. ( 1998 ). Module Theory , Progress in Mathematics , Vol. 167 . Basel : Birkhäuser Varlag . Endomorphism rings and direct sum decompositions in some classes of modules .
- Fakhruddin , S. M. ( 1973 ). Pure-injective modules . Glasgow Math. J. 18 : 120 – 122 .
- Faith , C. ( 1966 ). On Köthe rings . Math. Annalen 164 : 207 – 212 .
- Faith , C. , Walker , E. A. ( 1967 ). Direct sum representation of injective modules . J. Algebra 5 ( 2 ): 203 – 221 .
- Fuchs , L. , Salce , L. (2001). Modules Over Non-Noetherian Domain, Mathematical Surveys and Monographs . Providence : Amer. Math. Soc. , Vol. 84.
- Goodearl , K. R. ( 1976 ). Ring Theory: Nonsingular Rings and Modules . New York : Marcel Dekker .
- Goodearl , K. R. , Warfield , R. B. ( 2004 ). An Introduction to Noncommutative Noetherian Rings. , 2nd ed. Cambridge : Cambridge University Press .
- Gramopadhye , S. S. , Hiremath , V. A. ( 2009 ). Cyclic pure submodules . Int. J. Algebra 3 ( 3 ): 125 – 135 .
- Habeb , J. M. ( 1990 ). A note on zero commutative and duo rings . Math. J. Okayama Univ. 32 : 73 – 76 .
- Köthe , G. ( 1935 ). Verallgemeinerte abelsche gruppen mit hyperkomplexen operatorenring . Math. Z. 39 : 31 – 44 .
- Lam , T. Y. ( 1999 ). Lectures on Modules and Rings . Graduate Texts in Mathematics , Vol. 189 . New York : Springer-Verlag .
- Matsumura , H. 1989 . Commutative Ring Theory . Cambridge Studies in Advanced Mathematics, No. 8 . Cambridge : Cambridge University Press .
- Nakayama , T. ( 1940 ). Note on uni-serial and generalized uni-serial rings . Proc. Imp. Acad. Tokyo 16 : 285 – 289 .
- Naudé , C. G. , Naudé , G. , Pretorius , L. M. ( 1986 ). Equational characterization of relative injectivities . Comm. Algebra 14 : 39 – 48 .
- Osofsky , B. L. ( 1964 ). Rings all of whose finitely generated modules are injective . Pacific J. Math. 14 : 645 – 650 .
- Puninski , G. E. ( 1993 ). Rings defined by purities . Comm. Mosc. Math. Soc. , 181 – 182 .
- Puninski , G. , Prest , M. , Rothmaler , Ph. ( 1999 ). Rings described by various purities . Comm. Algebra 27 ( 5 ): 2127 – 2162 .
- Puninski , G. E. ( 1994 ). Warfield Rings . Algebra and logic 33 ( 3 ): 147 – 159 .
- Warfield , R. B. ( 1969 ). Purity and algebraic compactness for modules . Pacific J. Math. 28 : 699 – 719 .
- Warfield , R. B. ( 1969 ). Relative injective modules. Unpublished manuscript .
- Warfield , R. B. ( 1969 ). A Krull–Schmidt theorem for infinite sums of modules . Proc. Amer. Math. Soc. 22 : 460 – 465 .
- Warfield , R. B. ( 1970 ). Decomposability of finitely presented modules . Proc. Amer. Math. Soc. 25 : 167 – 172 .
- Warfield , R. B. ( 1975 ). Serial rings and finitely presented modules . J. Algebra 37 ( 2 ): 187 – 222 .
- Wisbauer , R. ( 1991 ). Foundations of Module and Ring Theory . New York : Gordon and Breach .
- Communicated by T. Albu.