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Dergiler / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 1

On pseudo semi-projective modules

Truong Cong QUYNH
Sayfa
27–36
Yayın Tarihi
2013-01-01
DOI
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Some properties of this class of module are studied.

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Amaç & Hipotez:A right R-module M is called semi-projective if, for any submodule N of M, every epimorphism p: M \rightarrow N and every homomorphism a: M \rightarrow N, there exists a homomorphism b: M \rightarrow M such that p b = a (see [11]).
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Temel Bulgular & Veri:In this paper, we consider some generalizations of semi-projective module, that is quasi pseudo principally projective module.
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Sonuç & Katkı:Some properties of this class of module are studied.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Key words: Semi-projective module · pseudo principally projective module · Key words: Semi-projective module

Özet

A right R-module M is called semi-projective if, for any submodule N of M, every epimorphism p: M \rightarrow N and every homomorphism a: M \rightarrow N, there exists a homomorphism b: M \rightarrow M such that p b = a (see [11]). In this paper, we consider some generalizations of semi-projective module, that is quasi pseudo principally projective module. Some properties of this class of module are studied.

Abstract

A right R-module M is called semi-projective if, for any submodule N of M, every epimorphism p: M \rightarrow N and every homomorphism a: M \rightarrow N, there exists a homomorphism b: M \rightarrow M such that p b = a (see [11]). In this paper, we consider some generalizations of semi-projective module, that is quasi pseudo principally projective module. Some properties of this class of module are studied.

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Bu Makaleye Atıf Yap

QUYNH, T. C. (2013). On pseudo semi-projective modules. Turkish Journal of Mathematics, Cilt: 37 - Sayı: 1, 27–36. https://ajindex.com/articles/185722

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Kaynakça (11)

  1. Anderson, F.W., and Fuller, K.R.: Rings and Categories of Modules. Springer-Verlag. New York 1974.
  2. Clark, J., Lomp, J., Vanaja, N. and Wisbauer, R.: Lifting Modules Supplements and Projectivity in Module Theory. Frontiers in Math. Boston. Birkh¨ auser. 2006.
  3. Dung, N.V., Huynh, D.V., Smith, P.F., and Wisbauer, R.: Extending Modules. Pitman 1996.
  4. Keskin, D.: A generalization of quasi-projective modules. Far East J. Math. Sci. 2, 483–488 (2000).
  5. Keskin, D., and Kuratomi, Y.: On epi-projective modules. East-West J. Math. 10, 27–35 (2008).
  6. Mohammed, S.H., and M¨ uller, B.J.: Continuous and Discrete Modules. London Math. Soc. LN 147. Cambridge Univ. Press. 1990.
  7. Nicholson, W.K., and Yousif, M.F.: Quasi-Frobenius Rings. Cambridge Univ. Press. 2003.
  8. Nicholson, W.K., Park, J.K. and Yousif, M.F.: Principally quasi-injective modules. Comm. Algebra 27, 1683–1693 (1999).
  9. Samruam, B., Hai, H.D., and Sanh, N.V.: On pseudo-P-injectivity. to appear in South. Asian Bull. Math. (2010).
  10. Sanh, N.V., Asawasamri, S., Ahmed, K.F., and Thao, P.L.: On prime and semiprime Goldie modules. AsianEuropean J. of Math. 4, 321–334 (2011).
  11. Wisbauer, R.: Foundations of Module and Ring Theory. Gordon and Breach. Reading 1991.