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- W2238631743 abstract "We construct an example of a unit-regular ring which is not strongly clean, answering an open question of Nicholson. We also characterize clean matrices with a zero column, and this allows us to describe an interesting connection between unit-regular elements and clean elements. It is also proven that given an element $a$ in a ring $R$, if $a,a^2,ldots, a^k$ are all regular elements in $R$ (for some $kgeq 1$), then there exists $win R$ such that $a^{i}w^{i}a^{i}=a^{i}$ for $1leq ileq k$, and a similar statement holds for unit-regular elements. The paper ends with a large number of examples elucidating further connections (and disconnections) between cleanliness, regularity, and unit-regularity." @default.
- W2238631743 created "2016-06-24" @default.
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- W2238631743 date "2015-10-12" @default.
- W2238631743 modified "2023-09-27" @default.
- W2238631743 title "Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings" @default.
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