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Original Articles

On Covers and Envelopes under Hom and Tensor Functors

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Pages 4334-4349 | Received 16 Jun 2013, Published online: 06 Jul 2015

REFERENCES

  • Anderson , F. W. , Fuller , K. R. ( 1974 ). Rings and Categories of Modules . New York : Springer-Verlag .
  • Asensio Mayor , J. , Martinez Hernandez , J. (1993). On flat and projective envelopes. J. Algebra 160:434–440.
  • Belshoff , R. G. , Xu , J. ( 1992 ). Injective envelopes and flat covers of Matlis reflexive modules . J. Pure Appl. Algebra 79 : 205 – 215 .
  • Bican , L. , Bashir , E. , Enochs , E. E. ( 2001 ). All modules have flat covers . Bull. London Math. Soc. 33 : 385 – 390 .
  • Colby , R. R. ( 1975 ). Rings which have flat injective modules . J. Algebra 35 : 239 – 252 .
  • Colby , R. R. , Fuller , K. R. ( 2004 ). Equivalence and Duality for Module Categories . Cambridge : Cambridge University Press .
  • Ding , N. Q. ( 1996 ). On envelopes with the unique mapping property . Comm. Algebra 24 : 1459 – 1470 .
  • Enochs , E. E. ( 1981 ). Injective and flat covers, envelopes and resolvents . Israel J. Math. 39 : 189 – 209 .
  • Enochs , E. E. , Jenda , O. M. G. ( 2000 ). Relative Homological Algebra . Berlin-New York : Walter de Gruyter .
  • Enochs , E. E. , Huang , Z. Y. ( 2012 ). Injective envelopes and (Gorenstein) flat covers . Algebr. Represent. Theory 15 : 1131 – 1145 .
  • García Rozas , J. R. , Torrecillas , B. ( 1996 ). Preserving and reflecting covers by functors. Applications to graded modules . J. Pure Appl. Algebra 112 : 91 – 107 .
  • García Rozas , J. R. , Torrecillas , B. ( 1997 ). Covers of modules over a fixed ring . J. Algebra 197 : 479 – 491 .
  • García Rozas , J. R. , Torrecillas , B. ( 1999 ). Preserving of covers by Hopf invariants . Comm. Algebra 27 : 1737 – 1750 .
  • Matlis , E. ( 1982 ). Commutative coherent rings . Canad. J. Math. 34 ( 6 ): 1240 – 1244 .
  • Rotman , J. J. ( 1979 ). An Introduction to Homological Algebra . New York : Academic Press .
  • Wisbauer , R. ( 1991 ). Foundations of Module and Ring Theory . Philadelphia : Gordon and Breach .
  • Xu , J. ( 1996 ). Flat Covers of Modules . Lecture Notes in Math. , Vol. 1634. Berlin–Heidelberg–New York : Springer-Verlag .
  • Xue , W. ( 1996 ). Injective envelopes and flat covers of modules over a commutative ring . J. Pure Appl. Algebra 109 : 213 – 220 .
  • Communicated by T. Albu.

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