Rings in which elements are sums of tripotents and nilpotents
2018 ◽
Vol 17
(03)
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pp. 1850042
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A ring [Formula: see text] is strongly 2-nil-clean if every element in [Formula: see text] is the sum of a tripotent and a nilpotent that commute. We prove that a ring [Formula: see text] is strongly 2-nil-clean if and only if [Formula: see text] is a strongly feebly clean 2-UU ring if and only if [Formula: see text] is an exchange 2-UU ring. Furthermore, we characterize strongly 2-nil-clean ring via involutions. We show that a ring [Formula: see text] is strongly 2-nil-clean if and only if every element in [Formula: see text] is the sum of an idempotent, an involution and a nilpotent that commute.
2015 ◽
Vol 14
(06)
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pp. 1550094
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2016 ◽
Vol 15
(08)
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pp. 1650148
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Vol 13
(06)
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pp. 1450009
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2017 ◽
Vol 16
(04)
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pp. 1750073
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2013 ◽
Vol 96
(2)
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pp. 258-274
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2016 ◽
Vol 15
(10)
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pp. 1620001
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2016 ◽
Vol 16
(07)
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pp. 1750135
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2007 ◽
Vol 06
(04)
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pp. 671-685
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2014 ◽
Vol 14
(01)
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pp. 1550004
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2012 ◽
Vol 40
(5)
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pp. 1595-1604
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