On strongly clean matrices over commutative clean rings

Burgess, W. D.

doi:10.48550/arxiv.1401.2052

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2014

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“…It is an attractive problem to express an element in a ring as the sum of idempotents and units (cf. [4], [6], [8] and [9]). We say that a ring R is clean provided that every element in R is the sum of an idempotent and a unit.…”

Section: Introductionmentioning

confidence: 99%

Periodicity and J-Clean-like Rings

Chen¹,

Abdolyousefi²

2014

Preprint

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A ring R is periodic provided that for any a ∈ R there exist distinct elements m, n ∈ N such that a m = a n . We shall prove that periodicity is inherited by all generalized matrix rings. A ring R is called strongly periodic if for any a ∈ R there exists a potent p ∈ R such that a − p is in its prime radical and ap = pa. A ring R is J-clean-like if for any a ∈ R there exists a potent p ∈ R such that a − p is in its Jacobson radical. Furthermore, we completely determine the connections between strongly periodic rings and periodic rings. The relations among J-clean-like rings and these rings are also obtained.

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Section: Introductionmentioning

confidence: 99%