A Multiplicative Dual Nil Q-Clean Rings

Year 2022, , 471 - 474, 31.08.2022

Tufan Özdin

https://doi.org/10.18185/erzifbed.1083173

Abstract

In this paper our goal to thoroughly determine the rings in which each non-unit element is a product of a nilpotent and a quasi-idempotent.

Keywords

Nilpotent Element, Nil-Clean Ring, Quasi-Idempotent Element, Nil Q-Rings.

References

• Breaz S., Călugăreanu G. G., Danchev P. and Micu T. 2013. “Nil-clean matrix rings”, Linear Algebra Appl., 439 (10), 3115–3119.
• Diesl A. J. 2013., “Nil clean rings”, J. Algebra, 383, 197–211.
• Kosan M. T., Lee T-K. and Zhou Y. 2014. “When is every matrix over a division ring a sum of an idempotent and a nilpotent?”, Linear Algebra Appl., 450, 7–12.
• Kosan T., Wang Z. and Zhou Y. 2016. “Nil-clean and strongly nil-clean rings”, J. Pure Appl. Algebra, 220 (2), 633–646.
• Nicholson W. K. 1977. “Lifting idempotents and exchange rings”, Trans. Amer. Math. Soc., 229, 269-278.
• Matczuk J. (2017), “Conjugate (nil) clean rings and Köthe’s problem”, J. Algebra Appl., 16 (4), Article 1750073. doi:10.1142/S0219498817500736
• Sahinkaya S., Tang G. and Zhou Y. 2017. “Nil-clean group rings”, J. Algebra Appl., 16 (7), (2017), Article 1750135. doi.org:10.1142/S0219498817501353
• Tang G., Su H. and Yuan P. 2021. “Quasi-clean rings and strongly quasi-clean rings”, Commun. Contemp. Math.. doi.org:10.1142/S0219199721500796
• Zhou Z. 2021. “A multiplicative dual of nil-clean rings”, Canadian Mathematical Bulletin, 1-5. doi:10.4153/S0008439521000059