Whether lcm splitting implies adequacy

Determine whether the lcm splitting property of a Bézout domain necessarily implies adequacy.

Background

Adequacy is shown to imply lcm splitting, while the paper constructs a pair in the domain R_V that violates adequacy but still satisfies lcm splitting. This pair-level distinction does not settle the ring-level implication, because a domain may have some non-adequate pairs while all pairs admit lcm splittings.