Strongly clean triangular matrices over abelian rings

Diesl, Alexander J.; Dorsey, Thomas J.; Iberkleid, Wolf; Lafuente-Rodriguez, Ramiro H.; McGovern, Warren Wm.

doi:10.1016/j.jpaa.2015.03.011

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Corollary 22 If R Is a Weakly Clean Ring With The Strong P1

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Cited by 4 publications

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“…Moreover, any strongly clean ring, being a clean ring equipped with the strong property, is also a weakly clean ring having the strong property; e.g., the triangular (upper or lower) matrix ring T n (R) is a non-commutative example of a strongly clean ring for all n ∈ N, whenever R is a commutative clean ring (cf. [28] and [19]).…”

Section: Corollary 22 If R Is a Weakly Clean Ring With The Strong Pmentioning

confidence: 98%

On weakly clean and weakly exchange rings having the strong property

Danchev

2017

Publ Inst Math (Belgr)

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We define two classes of rings calling them weakly clean rings and weakly exchange rings both equipped with the strong property. Although the classes of weakly clean rings and weakly exchange rings are different, their two proper subclasses above do coincide. This extends results due to W. Chen (Commun. Algebra, 2006) and Chin-Qua (Acta Math. Hungar., 2011). We also completely characterize strongly invo-regular rings, thus somewhat extending results due to Danchev-McGovern (J. Algebra, 2015). Some other principal results concerning weakly clean and weakly exchange rings are discussed as well.

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Section: Corollary 22 If R Is a Weakly Clean Ring With The Strong Pmentioning

confidence: 98%