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Journals / International Electronic Journal of Algebra / 2019 / Cilt: 26 - Sayı: 26

A GENERALIZATION OF SIMPLE-INJECTIVE RINGS

Zhu ZHANMİN
Pages
76–86
Publication Date
2019-07-11
DOI
—
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AI Summary & Key Takeaways

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

A ring R is called right 2-simple J-injective if, for every 2-generated

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A ring R is called right 2-simple J-injective if, for every 2-generated
📊
Key Findings & Data:A ring R is called right 2-simple J-injective if, for every 2-generated
💡
Conclusion & Impact:A ring R is called right 2-simple J-injective if, for every 2-generated
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:2-Simple J-injective ring · Kasch ring · semilocal ring

Abstract

A ring R is called right 2-simple J-injective if, for every 2-generated

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Cite This Article

ZHANMİN, Z. (2019). A GENERALIZATION OF SIMPLE-INJECTIVE RINGS. International Electronic Journal of Algebra, Cilt: 26 - Sayı: 26, 76–86. https://ajindex.com/articles/832288

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References (18)

  1. J. E. Bjork, Rings satisfying certain chain conditions, J. Reine Angew. Math., 245 (1970), 63-73.
  2. J. L. Chen, N. Q. Ding and M. F. Yousif, On Noetherian rings with essential socle, J. Aust. Math. Soc., 76 (2004), 39-49.
  3. J. L. Chen, Y. Q. Zhou and Z. M. Zhu, GP-injective rings need not be P-injective, Comm. Algebra, 33 (2005), 2395-2402. J. L. Gomez Pardo and P. A. Guil Asensio, Torsionless modules and rings with nite essential socle, Abelian groups, module theory, and topology (Padua, 1997), Lecture Notes in Pure and Appl. Math., Dekker, New York, 201 (1998), 261-278.
  4. M. Harada, Self mini-injective rings, Osaka J. Math. 19 (1982), 587-597.
  5. L. X. Mao, Min-flat modules and min-coherent rings, Comm. Algebra, 35 (2007), 635-650.
  6. W. K. Nicholson and M. F. Yousif, Principally injective rings, J. Algebra, 174 (1995), 77-93.
  7. W. K. Nicholson and M. F. Yousif, Mininjective rings, J. Algebra, 187 (1997), 548-578.
  8. W. K. Nicholson and M. F. Yousif, Quasi-Frobenius Rings, Cambridge Tracts in Mathematics, 158, Cambridge University Press, Cambridge, 2003.
  9. W. K. Nicholson, J. K. Park and M. F. Yousif, Extensions of simple-injective rings, Comm. Algebra, 28 (2000), 4665-4675.
  10. W. K. Nicholson, J. K. Park and M. F. Yousif, On simple-injective rings, Algebra Colloq., 9 (2002), 259-264.
  11. S. S. Page and Y. Q. Zhou, Generalizations of principally injective rings, J. Algebra, 206 (1998), 706-721.
  12. E. A. Rutter, Jr., Rings with the principal extension property, Comm. Algebra, 3 (1975), 203-212.
  13. L. Shen and J. L. Chen, New characterizations of quasi-Frobenius rings, Comm. Algebra, 34 (2006), 2157-2165.
  14. M. F. Yousif and Y. Q. Zhou, Rings for which certain elements have the principal extension property, Algebra Colloq., 10 (2003), 501-512.
  15. M. F. Yousif and Y. Q. Zhou, FP-injective, simple-injective, and quasi-Frobenius rings, Comm. Algebra, 32 (2004), 2273-2285.
  16. Y. Q. Zhou, Rings in which certain right ideals are direct summands of annihilators, J. Aust. Math. Soc., 73 (2002), 335-346. Z. M. Zhu and J. L. Chen, 2-Simple injective rings, Int. J. Algebra, 4 (2010), 25-37.
  17. Z. M. Zhu, MP-injective rings and MGP-injective rings, Indian J. Pure. Appl. Math., 41 (2010), 627-645.
  18. Z. M. Zhu, Some results on MP-injectivity and MGP-injectivity of rings and modules, Ukrainian Math. J., 63 (2012), 1623-1632.