2 problems

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Failure of the Cline formula for one-sided generalized Drazin inverses
Failure conjecture. The Cline formula may not hold for one-sided (generalized) Drazin inverses.
Conjectureopenbanach-algebras drazin-inverses spectral-theoryarXiv posted 2 days ago
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The strong $\pi$ -regularity conjecture for pseudo $\pi$ -polar $\pi$ -UU rings
Let $R$ be a ring. A ring is pseudo $\pi$ -polar if it satisfies the pseudo $\pi$ -polar condition, and $\pi$ -UU if every unit $u\in U(R)$ has $1-u^n\in J(R)$ for some integer…
Conjectureopendrazin-inverses regular-rings ring-theoryarXiv posted 2 days ago

Failure of the Cline formula for one-sided generalized Drazin inverses