Invo-regular unital rings
2018 ◽
Vol 72
(1)
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pp. 45
It was asked by Nicholson (Comm. Algebra, 1999) whether or not unit-regular rings are themselves strongly clean. Although they are clean as proved by Camillo-Khurana (Comm. Algebra, 2001), recently Nielsen and Ster showed in Trans. Amer. Math. Soc., 2018 that there exists a unit-regular ring which is not strongly clean. However, we define here a proper subclass of rings of the class of unit-regular rings, called invo-regular rings, and establish that they are strongly clean. Interestingly, without any concrete indications a priori, these rings are manifestly even commutative invo-clean as defined by the author in Commun. Korean Math. Soc., 2017.
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1986 ◽
Vol 38
(3)
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pp. 633-658
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1974 ◽
Vol 17
(2)
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pp. 283-284
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1971 ◽
Vol 23
(2)
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pp. 197-201
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2013 ◽
Vol 88
(3)
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pp. 499-505
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2020 ◽
Vol 1591
(1)
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pp. 012098
2019 ◽
Vol 19
(12)
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pp. 2050235
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