Dergiler / International Electronic Journal of Algebra / 2026 / Volume: 40 Issue: 40

Rings whose von Neumann regular elements are fine

Omar Almallah(Al-Balqa Applied University)
Grigore Călugăreanu(Babes-Bolyai University)
Sayfa
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Yayın Tarihi
2026-07-16
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This condition extends the notion of fine rings and identifies a distinguished subclass of idempotent-fine rings.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We study rings in which every von Neumann regular element is fine.
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Temel Bulgular & Veri:We study rings in which every von Neumann regular element is fine.
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Sonuç & Katkı:This condition extends the notion of fine rings and identifies a distinguished subclass of idempotent-fine rings.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:von Neumann regular · fine · RF ring

Abstract

We study rings in which every von Neumann regular element is fine. This condition extends the notion of fine rings and identifies a distinguished subclass of idempotent-fine rings.

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Bu Makaleye Atıf Yap

Almallah, O., Călugăreanu, G. (2026). Rings whose von Neumann regular elements are fine. International Electronic Journal of Algebra, Volume: 40 Issue: 40. https://doi.org/10.24330/ieja.1943809

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Kaynakça (14)

  1. D. Alpern, Quadratic equation solver, www.alpertron.com.ar/QUAD.HTM.
  2. G. Calugareanu and T. Y. Lam, Fine rings: A new class of simple rings, J. Algebra Appl., 15(9) (2016), 1650173 (18 pp).
  3. G. Calugareanu and Y. Zhou, Rings with fine idempotents, J. Algebra Appl., 21(1) (2022), 2250013 (14 pp).
  4. K. R. Goodearl, Von Neumann Regular Rings, Second edition, Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1991.
  5. D. Huylebrouck, Equivalence of von Neumann regular and idempotent matrices, Czechoslovak Math. J., 41(1) (1991), 44-50.
  6. D. Huylebrouck and J. Van Geel, Diagonalisation of idempotent matrices, J. Algebra, 105(1) (1987), 196-206.
  7. T. Y. Lam, A First Course in Noncommutative Rings, Second edition, Graduate Texts in Mathematics, 131, Springer-Verlag, New York, 2001.
  8. T. Y. Lam and R. G. Swan, Symplectic modules and von Neumann regular matrices over commutative rings, Advances in ring theory, Trends Math., Birkhäuser/Springer Basel AG, Basel (2010), 213-227.
  9. T.-K. Lee and Y. Zhou, On lifting of idempotents and semiregular endomorphism rings, Colloq. Math., 125(1) (2011), 99-113.
  10. K. Matthews, http://www.numbertheory.org/php/generalquadratic.html.
  11. W. K. Nicholson and Y. Zhou, Strong lifting, J. Algebra, 285(2) (2005), 795-818.
  12. R. Puystjens and J. Van Geel, On the diagonalisation of von Neumann regular matrices, Acta Univ. Carolin. Math. Phys., 26(2) (1985), 51-56.
  13. G. Song and X. Guo, Diagonability of idempotent matrices over noncommutative rings, Linear Algebra Appl., 297 (1999), 1-7.
  14. A. Steger, Diagonability of idempotent matrices, Pacific J. Math., 19(3) (1966), 535-542.