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$\sqrtΔ$-Fine Rings
We introduce and study the so-termed {\it $\sqrtΔ$-fine rings}, a new class of rings that generalizes the classical {\it fine rings} introduced by Călugăreanu-Lam in J. Algebra \& Appl. (2016) by requiring that every nonzero element $r \in R$ can be written as $r = u + a$, where $u$ is a unit and $a
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