2 problems

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Unit regularity conjecture for proatomic $*$ -regular rings
Unit-regularity conjecture. If $R$ is $*$ -regular and $\overline{L}(R)$ is proatomic with an orthogonal large partial $n$ -frame, then $R$ is unit regular. Every representable ring…
Conjectureopenmodular-ortholattices regular-rings star-regular-ringsarXiv posted 2 days ago
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Representable $*$ -regular rings and ultraproducts of artinian rings
Representable-ring ultraproduct conjecture. Every subdirectly irreducible representable $*$ -regular ring can be embedded into a homomorphic image of a regular $*$ -subring of an ult…
Conjectureopenregular-rings star-regular-rings ultraproductsarXiv posted 2 days ago

Unit regularity conjecture for proatomic ∗*∗-regular rings