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Basic notions

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Lifting Modules

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References

  1. Brodskiř, G. M. and Wisbauer, R., General distributivity and thickness of modules, Arabian J. Sci. Eng. 25(2C), 95–128 (2000).

    Google Scholar 

  2. Lomp, Ch., On dual Goldie dimension, Diploma Thesis, University of Düsseldorf (1996).

    Google Scholar 

  3. Miyashita, Y., Quasi-projective modules, perfect modules, and a theorem for modular lattices, J. Fac. Sci. Hokkaido 19, 86–110 (1966).

    MATH  MathSciNet  Google Scholar 

  4. Oshiro, K., Semiperfect modules and quasi-semiperfect modules, Osaka J. Math. 20, 337–372 (1983).

    MATH  MathSciNet  Google Scholar 

  5. Reiter, E., A dual to the Goldie ascending chain condition on direct sums of submodules, Bull. Calcutta Math. Soc. 73, 55–63 (1981).

    MATH  MathSciNet  Google Scholar 

  6. Renault, G., Étude des sous-modules complements dans un module, Bull. Soc. Math. France Mém. 9 (1967).

    Google Scholar 

  7. Takeuchi, T., On cofinite-dimensional modules, Hokkaido Math. J. 5, 1–43 (1976).

    MathSciNet  Google Scholar 

  8. Wisbauer, R., Foundations of Module and Ring Theory, Gordon and Breach, Reading (1991). Grundlagen der Modul-und Ringtheorie, Verlag Reinhard Fischer, München (1988).

    MATH  Google Scholar 

  9. Zelinksy, D., Linearly compact modules and rings, Amer. J. Math. 75, 75–90 (1953).

    Google Scholar 

References

  1. Al-Khazzi, I. and Smith, P. F., Modules with chain conditions on superfluous submodules, Comm. Algebra 19, 2331–2351 (1991).

    MATH  MathSciNet  Google Scholar 

  2. Faith, C., Rings whose modules have maximal submodules, Publ. Mat. 39, 201–214 (1995). Addendum, Publ. Mat. 42, 265–266 (1998).

    MATH  MathSciNet  Google Scholar 

  3. Generalov, A. I., ω-cohigh purity in the category of modules, Math. Notes 33, 402–408 (1983); translation from Mat. Zametki 33, 785–796 (1983).

    MATH  MathSciNet  Google Scholar 

  4. Golan, J. S., Quasiperfect modules, Quart. J. Math. Oxford (2), 22, 173–182 (1971).

    MATH  MathSciNet  Google Scholar 

  5. Harada, M., A note on hollow modules, Rev. Un. Mat. Argentina 28, 186–194 (1977/78).

    MathSciNet  Google Scholar 

  6. Hirano, Y., On rings over which each module has a maximal submodule, Comm. Algebra 26, 3435–3445 (1998).

    MATH  MathSciNet  Google Scholar 

  7. Inoue, T., Sum of hollow modules, Osaka J. Math. 20, 331–336 (1983).

    MATH  MathSciNet  Google Scholar 

  8. Leonard, W. W., Small modules, Proc. Amer. Math. Soc. 17, 527–531 (1966).

    Article  MATH  MathSciNet  Google Scholar 

  9. Pareigis, B., Radikale und kleine Moduln, Bayer. Akad. Wiss. Math.-Natur. Kl. S.-B. 1965, 1966 Abt. II, 185–199 (1966).

    Google Scholar 

  10. Rayar, M., On small and cosmall modules, Acta Math. Acad. Sci. Hungar. 39, 389–392 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  11. Renault, G., Sur les anneaux A tels que tout A-module à gauche non nul contient un sous-module maximal, C. R. Acad. Sci., Paris, Sér. A 267, 792–794 (1968).

    MATH  MathSciNet  Google Scholar 

  12. Takeuchi, T., On cofinite-dimensional modules, Hokkaido Math. J. 5, 1–43 (1976).

    MathSciNet  Google Scholar 

  13. Talebi, Y. and Vanaja, N., Copolyform modules, Comm. Algebra 30, 1461–1473 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  14. Tuganbaev, A. A., Rings whose nonzero modules have maximal submodules, J. Math. Sci. (New York) 109(3), 1589–1640 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  15. Wisbauer, R., Foundations of Module and Ring Theory, Gordon and Breach, Reading (1991). Grundlagen der Modul-und Ringtheorie, Verlag Reinhard Fischer, München (1988).

    MATH  Google Scholar 

References

  1. Chamard, J.-Y., Modules quasi-projectifs, projectifs et parfaits, Séminaire Dubreil-Pisot, Algèbre et Théorie des Nombres, 21e année, Nr. 8 (1967/68).

    Google Scholar 

  2. Ganesan, L. and Vanaja, N., Modules for which every submodule has a unique coclosure, Comm. Algebra 30, 2355–2377 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  3. Golan, J. S., Quasiperfect modules, Quart. J. Math. Oxford (2), 22, 173–182 (1971).

    MATH  MathSciNet  Google Scholar 

  4. Keskin, D., On lifting modules, Comm. Algebra 28, 3427–3440 (2000).

    MATH  MathSciNet  Google Scholar 

  5. Lomp, Ch., On dual Goldie dimension, Diploma Thesis, University of Düsseldorf (1996).

    Google Scholar 

  6. Reiter, E., A dual to the Goldie ascending chain condition on direct sums of submodules, Bull. Calcutta Math. Soc. 73, 55–63 (1981).

    MATH  MathSciNet  Google Scholar 

  7. Takeuchi, T., On cofinite-dimensional modules, Hokkaido Math. J. 5, 1–43 (1976).

    MathSciNet  Google Scholar 

  8. Talebi, Y. and Vanaja, N., Copolyform modules, Comm. Algebra 30, 1461–1473 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  9. Wisbauer, R., Foundations of Module and Ring Theory, Gordon and Breach, Reading (1991). Grundlagen der Modul-und Ringtheorie, Verlag Reinhard Fischer, München (1988).

    MATH  Google Scholar 

  10. Zöschinger, H., Minimax-Moduln, J. Algebra 102, 1–32 (1986).

    Article  MATH  MathSciNet  Google Scholar 

References

  1. Faticoni, T., On quasiprojective covers, Trans. Amer. Math. Soc. 278, 101–113 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  2. Golan, J. S., Quasiperfect modules, Quart. J. Math. Oxford (2), 22, 173–182 (1971).

    MATH  MathSciNet  Google Scholar 

  3. Golan, J. S., Characterization of rings using quasiprojective modules. II, Proc. Amer. Math. Soc. 28, 337–343 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  4. Goodearl, K. R., Surjective endomorphisms of finitely generated modules, Comm. Algebra 15, 589–609 (1987).

    MATH  MathSciNet  Google Scholar 

  5. Harada, M. and Mabuchi, T., On almost M-projectives, Osaka J. Math. 26, 837–848 (1989).

    MATH  MathSciNet  Google Scholar 

  6. Keskin, D., Discrete and quasi-discrete modules, Comm. Algebra 30, 5273–5282 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  7. Kuratomi, Y., On direct sum of lifting modules and internal exchange property, Comm. Algebra 33, 1795–1804 (2005).

    MATH  MathSciNet  Google Scholar 

  8. Lomp, Ch., On dual Goldie dimension, Diploma Thesis, University of Düsseldorf (1996).

    Google Scholar 

  9. Mohamed, S. H. and Müller, B. J., Cojective modules, J. Egyptian Math. Sci. 12, 83–96 (2004).

    MATH  Google Scholar 

  10. Talebi, Y. and Vanaja, N., Copolyform modules, Comm. Algebra 30, 1461–1473 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  11. Tiwary, A. K. and Pandeya, B.M., Pseudo projective and pseudo injective modules, Indian J. Pure Appl. Math. 9, 941–949 (1978).

    MATH  MathSciNet  Google Scholar 

  12. Varadarajan, K., Study of Hopficity in certain classes of rings, Comm. Algebra 28, 771–783 (2000).

    MATH  MathSciNet  Google Scholar 

  13. Vasconcelos, W., On finitely generated flat modules, Trans. Amer. Math. Soc. 138, 505–512 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  14. Wisbauer, R., Foundations of Module and Ring Theory, Gordon and Breach, Reading (1991). Grundlagen der Modul-und Ringtheorie, Verlag Reinhard Fischer, München (1988).

    MATH  Google Scholar 

References

  1. Fleury, P., A note on dualizing Goldie dimension, Canad. Math. Bull. 17, 511–517 (1974).

    MATH  MathSciNet  Google Scholar 

  2. Grezeszcuk, P. and Puczy lowski, E. R., On Goldie and dual Goldie dimension, J. Pure Appl. Algebra 31, 47–54 (1984).

    Article  MathSciNet  Google Scholar 

  3. Hanna, A. and Shamsuddin, A., Duality in the category of modules. Applications, Algebra Berichte 49, Verlag Reinhard Fischer, München (1984).

    Google Scholar 

  4. Hanna, A. and Shamsuddin, A., Dual Goldie dimension, Rend. Istit. Mat. Univ. Trieste 24, 25–38 (1994).

    MathSciNet  Google Scholar 

  5. Miyashita, Y., Quasi-projective modules, perfect modules, and a theorem for modular lattices, J. Fac. Sci. Hokkaido 19, 86–110 (1966).

    MATH  MathSciNet  Google Scholar 

  6. Page, S. S., Relatively semiperfect rings and corank of modules, Comm. Algebra 21, 975–990 (1993).

    MATH  MathSciNet  Google Scholar 

  7. Park, Y. S. and Rim, S. H., Hollow modules and corank relative to a torsion theory, J. Korean Math. Soc. 31, 439–456 (1994).

    MATH  MathSciNet  Google Scholar 

  8. Rangaswamy, K. M., Modules with finite spanning dimension, Canad. Math. Bull. 20, 255–262 (1977).

    MATH  MathSciNet  Google Scholar 

  9. Reiter, E., A dual to the Goldie ascending chain condition on direct sums of submodules, Bull. Calcutta Math. Soc. 73, 55–63 (1981).

    MATH  MathSciNet  Google Scholar 

  10. Rim, S. H. and Takemori, K., On dual Goldie dimension, Comm. Algebra 21, 665–674 (1993).

    MATH  MathSciNet  Google Scholar 

  11. Sarath, B. and Varadarajan, K., Dual Goldie dimension II, Comm. Algebra 7, 1885–1899 (1979).

    MATH  MathSciNet  Google Scholar 

  12. Takeuchi, T., On cofinite-dimensional modules, Hokkaido Math. J. 5, 1–43 (1976).

    MathSciNet  Google Scholar 

  13. Varadarajan, K., Dual Goldie dimension, Comm. Algebra 7, 565–610 (1979).

    MATH  MathSciNet  Google Scholar 

  14. Varadarajan, K., Modules with supplements, Pacific J. Math. 82, 559–564 (1979).

    MATH  MathSciNet  Google Scholar 

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(2006). Basic notions. In: Lifting Modules. Frontiers in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7573-6_1

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