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$\ast $-CLEAN RINGS
A 
$\ast $-ring 
$R$ is called (strongly) 
$\ast $-clean if every element of 
$R$ is the sum of a unit and a projection (that commute). Vaš [‘
$\ast $-Clean rings; some clean and almost clean Baer 
$\ast $-rings and von Neumann algebras’, J. Algebra 324(12) (2010), 3388–3400] asked whether there exists a 
$\ast $-ring that is clean but not 
$\ast $-clean and whether a unit regular and 
$\ast $-regular ring is strongly 
$\ast $-clean. In this paper, we answer these two questions. We also give some characterisations related to 
$\ast $-regular rings.
