2 problems

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…

Representable-ring ultraproduct conjecture. Every subdirectly irreducible representable $*$-regular ring can be embedded into a homomorphic image of a regular $*$-subring of an ult…