A class of projectively full ideals in two-dimensional Muhly local domains

Let (R,M) be a regular local domain of dimension d⩾2 and let x1,…,xd be a regular system of parameters. Then, Ciuperca, Heinzer, Ratliff Jr., and Rush have proved that every ideal of the form with n∈N+, is projectively full.If (R,M) is a two-dimensional Muhly local domain (i.e., an integrally closed Noetherian local domain with algebraically closed residue field and the associated graded ring an integrally closed domain), then we are able to prove a similar result for every minimal ideal basis x1,…,xd of M such that x1∉rad(x2,…,xd).