Geodesic
Rings whose Elements are the Sum of a Tripotent and an Element from the Jacobson Radical
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 810-821

Voir la notice de l'article provenant de la source Cambridge University Press

This paper is about rings $R$ for which every element is a sum of a tripotent and an element from the Jacobson radical $J(R)$. These rings are called semi-tripotent rings. Examples include Boolean rings, strongly nil-clean rings, strongly 2-nil-clean rings, and semi-boolean rings. Here, many characterizations of semi-tripotent rings are obtained. Necessary and sufficient conditions for a Morita context (respectively, for a group ring of an abelian group or a locally finite nilpotent group) to be semi-tripotent are proved.
DOI : 10.4153/S0008439519000092
Mots-clés : idempotent, tripotent, Jacobson radical, idempotent lifting modulo Jacobson radical, Boolean ring, semi-boolean ring 
Koşan, M. Tamer; Yildirim, Tülay; Zhou, Y. Rings whose Elements are the Sum of a Tripotent and an Element from the Jacobson Radical. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 810-821. doi: 10.4153/S0008439519000092
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[1] Burgess, W. D. and Raphael, R., On commutative clean rings and pm rings . In: Rings, Modules and Representations , Contemp. Math., 480, Amer. Math. Soc., Providence, RI, 2009, pp. 35–55. Google Scholar

[2] Chen, H., On strongly J-clean rings . Commun. Algebra 38(2010), 3790–3804. Google Scholar

[3] Chen, H. and Sheibani, M., Strongly 2-nil-clean rings . J. Algebra Appl. 16(2017), 1750178 (12 pages). Google Scholar

[4] Connell, I. G., On the group ring . Canad. J. Math. 15(1963), 650–685. Google Scholar

[5] Diesl, A. J., Nil clean rings . J. Algebra 383(2013), 197–211. Google Scholar

[6] Hirano, Y. and Tominaga, H., Rings in which every element is the sum of two idempotents . Bull. Austral. Math. Soc. 37(1988), 161–164. Google Scholar

[7] Khurana, D., Lam, T. Y., and Nielsen, P. P., Exchange rings, exchange equations, and lifting properties . Internat. J. Algebra Comput. 26(2016), 1177–1198. Google Scholar

[8] Koşan, T., Leroy, A., and Matczuk, J., On UJ-rings . Commun. Algebra 46(2018), 2297–2303. Google Scholar

[9] Koşan, T., Wang, Z., and Zhou, Y., Nil-clean and strongly nil-clean rings . J. Pure Appl. Algebra 220(2016), 633–646. Google Scholar

[10] Lee, T. K. and Zhou, Y., A class of exchange rings . Glasgow Math. J. 50(2008), 509–522. Google Scholar

[11] Levitzki, J., On the structure of algebraic algebras and related rings . Trans. Amer. Math. Soc. 74(1953), 384–409. Google Scholar

[12] Matczuk, J., Conjugate (nil) clean rings and Köthe’s conjecture . J. Algebra Appl. 16(2017), 1750073 (14 pages). Google Scholar

[13] Mazurek, R., Nielsen, P. P., and Ziembowski, M., Commuting idempotents, square-free modules, and the exchange property . J. Algebra 444(2015), 52–80. Google Scholar

[14] Nicholson, W. K., Lifting idempotents and exchange rings . Trans. Amer. Math. Soc. 229(1977), 269–278. Google Scholar

[15] Nicholson, W. K. and Zhou, Y., Clean general rings . J. Algebra 291(2005), 297–311. Google Scholar

[16] Nicholson, W. K. and Zhou, Y., Strong lifting . J. Algebra 285(2005), 795–818. Google Scholar

[17] Sands, A. D., Radicals and Morita contexts . J. Algebra 24(1973), 335–345. Google Scholar

[18] Zhou, Y., On clean group rings . In: Advances in Ring Theory , Trends in Mathematics, Birkhäuser, Verlag Basel/Switzerland, 2010, pp. 335–345. Google Scholar

[19] Zhou, Y., Rings in which elements are sums of nilpotents, idempotents and tripotents . J. Algebra Appl. 17(2018), 1850009 (7 pages). Google Scholar

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