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Unipotent and Unit-Regular Elements in Certain Subrings of M_2 (Z)

Year 2023, Volume: 16 Issue: 1, 286 - 294, 31.03.2023
https://doi.org/10.18185/erzifbed.1213747

Abstract

We presented a simple and direct way to construct a unipotent unit and clean but not nil-clean element in a ring. New examples of unipotent/unit-regular elements that are not nil-clean are given. We also study the product of two idempotents/unit-regulars which are unit-regular. The studies are exemplified in two subrings of M_2 (Z).

References

  • Andrica D., Călugăreanu G.G., (2014) A nil-clean 2×2 matrix over the integers which is not clean, J. Algebra, 13(6), 3115–3119. doi:10.1142/S0219498814500091
  • Călugăreanu, G., Lam, T.Y., (2015) Fine rings: A new class of simple rings, J. Algebra Appl., 15(9), 1650173-18 pages. doi:10.1142/S0219498816501735
  • Călugăreanu, G., (2015) UU rings, Carpathian J. Math., 31(2), 157-163. doi:10.37193/CJM.2015.02.02
  • Călugăreanu, G., Pob, H.F. On stable range one matrices, Preprint
  • Garcia, J.L., (1989) Properties of direct summands of modules, Commun. Algebra, 17, 73–92. doi: 10.1080/00927878908823714
  • Khurana, D., Lam, T.Y., (2004) Clean matrices and unit-regular matrices, J. Algebra, 280, 683-698. doi:10.1016/j.jalgebra.2004.04.019
  • Nicholson W. K., (1977) Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229, 269-278. doi:10.1090/S0002-9947-1977-0439876-2
  • Wu, Y., Tang, G., Deng, G., Zhou, Y., (2019) Nil-clean and unit-regular elements in certain subrings of M_2 (Z), Czechoslovak Math. J., 69(1), 197-205. doi:10.21136/CMJ.2018.0256-17

M_2 (Z) Halkasının Belirli Alt Halkalarındaki Tek Kuvvetli ve Terslenir Düzenli Elemanlar

Year 2023, Volume: 16 Issue: 1, 286 - 294, 31.03.2023
https://doi.org/10.18185/erzifbed.1213747

Abstract

Bir halkada, bir sıfır güçlü terslenir ve temiz ama nil-temiz olmayan bir eleman oluşturmanın basit ve doğrudan bir yolunu sunduk. Nil-temiz olmayan sıfır güçlü/terslenir-düzenli elemanların yeni örnekleri verilmiştir. Ayrıca, terslenir-düzenli olan iki eşkare/birim-düzenli elemanların çarpımları da incelenmiştir. M_2 (Z) halkasının iki alt halkasında çalışmalar örneklendirilmiştir.

References

  • Andrica D., Călugăreanu G.G., (2014) A nil-clean 2×2 matrix over the integers which is not clean, J. Algebra, 13(6), 3115–3119. doi:10.1142/S0219498814500091
  • Călugăreanu, G., Lam, T.Y., (2015) Fine rings: A new class of simple rings, J. Algebra Appl., 15(9), 1650173-18 pages. doi:10.1142/S0219498816501735
  • Călugăreanu, G., (2015) UU rings, Carpathian J. Math., 31(2), 157-163. doi:10.37193/CJM.2015.02.02
  • Călugăreanu, G., Pob, H.F. On stable range one matrices, Preprint
  • Garcia, J.L., (1989) Properties of direct summands of modules, Commun. Algebra, 17, 73–92. doi: 10.1080/00927878908823714
  • Khurana, D., Lam, T.Y., (2004) Clean matrices and unit-regular matrices, J. Algebra, 280, 683-698. doi:10.1016/j.jalgebra.2004.04.019
  • Nicholson W. K., (1977) Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229, 269-278. doi:10.1090/S0002-9947-1977-0439876-2
  • Wu, Y., Tang, G., Deng, G., Zhou, Y., (2019) Nil-clean and unit-regular elements in certain subrings of M_2 (Z), Czechoslovak Math. J., 69(1), 197-205. doi:10.21136/CMJ.2018.0256-17
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

Günseli Gümüşel 0000-0001-8068-4294

Early Pub Date March 29, 2023
Publication Date March 31, 2023
Published in Issue Year 2023 Volume: 16 Issue: 1

Cite

APA Gümüşel, G. (2023). Unipotent and Unit-Regular Elements in Certain Subrings of M_2 (Z). Erzincan University Journal of Science and Technology, 16(1), 286-294. https://doi.org/10.18185/erzifbed.1213747