3 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…

Exceptional-frame conjecture. There are subdirectly irreducible coordinatizable MOLs of height at least $3$ not containing an orthogonal large partial $n$-frame.

Geometric representation conjecture. The von Neumann example of a continuous geometry admits a geometric representation over an elementary extension of the reals.