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A multiplicative dual of nil-clean rings

Part of: Conditions on elements Rings and algebras arising under various constructions Local rings and generalizations

Published online by Cambridge University Press:  09 February 2021

Yiqiang Zhou
Yiqiang Zhou*
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NLA1C 5S7, Canada
*
e-mail: zhou@mun.ca
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Abstract

The goal of this note is to completely determine the rings for which every nonunit is a product of a nilpotent and an idempotent (in either order).

Keywords

Idempotentnilpotentnil-clean ringdual nil-clean ring

MSC classification

Primary: 16U99: None of the above, but in this section
Secondary: 16L30: Noncommutative local and semilocal rings, perfect rings 16S50: Endomorphism rings; matrix rings
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 1 , March 2022 , pp. 39 - 43
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Copyright
© Canadian Mathematical Society 2021

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References

Breaz, S., Cǎlugǎreanu, G., Danchev, P., and Micu, T., Nil-clean matrix rings. Linear Algebra Appl. 439(2013), 3115–3119.CrossRefGoogle Scholar
Cǎlugǎreanu, G., UN-rings. J. Algebra Appl. 15(2016), 1650182, 9 pp.10.1142/S0219498816501826CrossRefGoogle Scholar
Cǎlugǎreanu, G. and Lam, T. Y., Fine rings: a new class of simple rings. J. Algebra Appl. 15(2016), 1650173, 18 pp.10.1142/S0219498816501735CrossRefGoogle Scholar
Chen, J., Yang, X., and Zhou, Y., On strongly clean matrix and triangular matrix rings. Comm. Algebra 34(2006), 3659–3674.10.1080/00927870600860791CrossRefGoogle Scholar
Diesl, A. J., Nil clean rings. J. Algebra 383(2013), 197–211.10.1016/j.jalgebra.2013.02.020CrossRefGoogle Scholar
Kosan, M. T., Lee, T. -K., and Zhou, Y., When is every matrix over a division ring a sum of an idempotent and a nilpotent? Linear Algebra Appl. 450(2014), 7–12.10.1016/j.laa.2014.02.047CrossRefGoogle Scholar
Kosan, T., Wang, Z., and Zhou, Y., Nil-clean and strongly nil-clean rings. J. Pure Appl. Algebra 220(2016), 633–646.10.1016/j.jpaa.2015.07.009CrossRefGoogle Scholar
Matczuk, J., Conjugate (nil) clean rings and Köthe’s problem. J. Algebra Appl. 16(2017), 1750073, 14 pp.10.1142/S0219498817500736CrossRefGoogle Scholar
McGovern, W. W., Raja, S., and Sharp, A., Commutative nil clean group rings. J. Algebra Appl. 14(2015), 1550094, 5 pp.10.1142/S0219498815500942CrossRefGoogle Scholar
Nicholson, W. K., Lifting idempotents and exchange rings. Trans. Amer. Math. Soc. 229(1977), 269–278.10.1090/S0002-9947-1977-0439876-2CrossRefGoogle Scholar
Robson, J. C., Recognition of matrix rings. Comm. Algebra 19(1991), 2113–2124.10.1080/00927879108824248CrossRefGoogle Scholar
Sahinkaya, S., Tang, G., and Zhou, Y., Nil-clean group rings. J. Algebra Appl. 16(2017), 1750135, 7 pp.10.1142/S0219498817501353CrossRefGoogle Scholar