TWO QUESTIONS OF L. VAŠ ON -CLEAN RINGS
2013 ◽
Vol 88
(3)
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pp. 499-505
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AbstractA $\ast $-ring $R$ is called (strongly) $\ast $-clean if every element of $R$ is the sum of a unit and a projection (that commute). Vaš [‘$\ast $-Clean rings; some clean and almost clean Baer $\ast $-rings and von Neumann algebras’, J. Algebra 324(12) (2010), 3388–3400] asked whether there exists a $\ast $-ring that is clean but not $\ast $-clean and whether a unit regular and $\ast $-regular ring is strongly $\ast $-clean. In this paper, we answer these two questions. We also give some characterisations related to $\ast $-regular rings.
1974 ◽
Vol 17
(2)
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pp. 283-284
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2006 ◽
Vol 2006
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pp. 1-6
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1971 ◽
Vol 4
(1)
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pp. 57-62
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1969 ◽
Vol 12
(4)
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pp. 417-426
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2011 ◽
Vol 10
(06)
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pp. 1363-1370
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2010 ◽
Vol 324
(12)
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pp. 3388-3400
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2016 ◽
Vol 26
(06)
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pp. 1177-1198
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