Amalgamated Rings with n-UJ-Properties

This paper examines the transfer of n­UJ-rings between A and B in an amalgamated duplication of a ring A along some ideal K of a ring B with a ring homomorphism f:A→B (denoted by A⋈^f K).

___

  • Anderson, D. D., Bennis, D., Fahid, B., & Shaiea, A. (2017). On n-trivial extension of rings. Rocky Mountain J. Math., 47(8), 2439-2511. doi:10.1216/RMJ-2017-47-8-2439
  • Calugareanu, G. (2015). UU rings. Carpathian J. Math., 31(2), 157-163. doi:10.37193/CJM.2015.02.02
  • Chen, H. (2010). On strongly J-clean rings. Communications in Algebra, 38(10), 3790-3804. doi:10.1080/00927870903286835
  • D’Anna, M., Finocchiaro, C. A., & Fontana, M. (2009). Amalgamated algebras along an ideal. In: M. Fontana, S-E. Kabbaj, B. Olberding & I. Swanson (Eds.), Commutative Algebra and Its Applications, Proceedings of the Fifth International Fez Conference on Commutative Algebra and Applications, Morocco, June 23-28, 2008, (pp. 155-172), De Gruyter, Berlin. doi:10.1515/9783110213188.155
  • Diesl, A. J. (2013). Nil clean rings. Journal of Algebra, 383, 197-211. doi:10.1016/j.jalgebra.2013.02.020
  • Farshad, N., SafariSabet, S. A., & Moussavi, A. (2021). Amalgamated rings with clean-type properties. Hacettepe J. Mathematics and Statistics, 50(5), 1358-1370. doi:10.15672/hujms.676342
  • Koşan, M. T., Leroy, A., & Matczuk, J. (2018). On UJ-rings. Communications in Algebra, 46(5), 2297-2303. doi:10.1080/00927872.2017.1388814
  • Koşan, M. T., Quynh, T. C., & Yildirim, T. (2020). Rings such that, for each unit u,u-u^n belongs to the Jacobson radical. Hacettepe J. Mathematics and Statistics, 49(4), 1397-1404. doi:10.15672/hujms.542574
  • Nicholson, W. K. (1977). Lifting idempotents and exchange rings. Trans. Amer. Math. Soc., 229, 269-278. doi:10.1090/S0002-9947-1977-0439876-2