Strongly unit nil-clean rings
2017 ◽
Vol 16
(06)
◽
pp. 1750115
An element in a ring is strongly nil-clean, if it is the sum of an idempotent and a nilpotent element that commute. A ring [Formula: see text] is strongly unit nil-clean, if for any [Formula: see text] there exists a unit [Formula: see text], such that [Formula: see text] is strongly nil-clean. We prove, in this paper, that a ring [Formula: see text] is strongly unit nil-clean, if and only if every element in [Formula: see text] is equivalent to a strongly nil-clean element, if and only if for any [Formula: see text], there exists a unit [Formula: see text], such that [Formula: see text] is strongly [Formula: see text]-regular. Strongly unit nil-clean matrix rings are investigated as well.
2019 ◽
Vol 18
(03)
◽
pp. 1950050
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2016 ◽
Vol 15
(09)
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pp. 1650173
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Keyword(s):
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2013 ◽
Vol 13
(03)
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pp. 1350109
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2012 ◽
Vol 12
(01)
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pp. 1250126
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Keyword(s):
Keyword(s):
2017 ◽
Vol 16
(10)
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pp. 1750197
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2019 ◽
Vol 18
(02)
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pp. 1950021