SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 2

Cofinitely injective and projective modules

C. NEBİYEV
A. PANCAR
Pages
171–182
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

If every cofinitely M-projective (M-injective) module is M-projective (M-injective) then RadM $neq$ M.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, cofinitely injective and cofinitely projective modules are defined.
📊
Key Findings & Data:Some properties of cofinitely injective and cofinitely projec- tive modules are investigated.
💡
Conclusion & Impact:If every cofinitely M-projective (M-injective) module is M-projective (M-injective) then RadM $neq$ M.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this work, cofinitely injective and cofinitely projective modules are defined. Some properties of cofinitely injective and cofinitely projec- tive modules are investigated. Let N be an R-module. Then every R-module is cofinitely N-injective if and only if every cofinite submod- ule of N is a direct summand. This is also true for cofinitely pro- jective modules. Let M be a nonzero R-module. If every cofinitely M-projective (M-injective) module is M-projective (M-injective) then RadM $neq$ M.

🔖

Cite This Article

NEBİYEV, C., PANCAR, A. (2022). Cofinitely injective and projective modules. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 2, 171–182. https://ajindex.com/articles/530623

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. Alizade, R., Bilhan, G. and Smith, P.F. Modules whose maximal submodules have supple- ments, Communications in Algebra 29 (6), 2389–2405, 2001
  2. Alizade, R. and B¨uy¨uka¸sık, E. Cofinitely weak supplemented modules, Communications in Algebra 13, 5377–5390, 2003
  3. Clark, J., Lomp, C., Vanaja, N. and Wisbauer, R. Lifting Modules (Birkh¨auser Verlag, Berlin, 2006)
  4. Hiremath, V.A. On cofinitely injective modules, J. London Math. Soc. (2) 17 (1), 28–32, 1978
  5. Hiremath, V.A. Cofinitely projective modules, Houston J. Math. 11 (2), 183–190, 1985
  6. Hiremath, V.A. Cofinitely projective modules II, Arch. Math. (Basel) 48 (1), 53–57, 1987
  7. Kaplansky, I. Projective modules, Ann. Math. 68, 372–377, 1958
  8. Mohamed, S.H. and M¨uller, B. J. Continuous and Discrete Modules (London Math. Soc. LNS 147, Cambridge Univ. Press, Cambridge, 1990)
  9. Wang, M.Y. and Zhao, G. On maximal injectivity, Acta Mathematica Sinica (English Series) 21 (6), 1451–1458, 2005
  10. Wisbauer, R. Foundations of Module and Ring Theory (Gordon and Breach, Philadelphia, 1991).