Star operations and primitive polynomials

Let D be an integral domain with quotient field K. We investigate condition s under which certain primitive polynomials are products of principal prime s. Let * be a finite character star operation on D[X] (e.g., * = d or t) an d let * also denote the star operation induced on D by I* = (I[X])* boolean AND K where I denotes a nonzero fractional ideal of D. Then the following conditions are equivalent: (1) D is integrally closed and each *-invertible *-ideal is principal, (2) If P is a, prime upper to 0 containing an f is a n element of D[X] with A(f)* = D, then P is principal, and (3) For f is an element of D[X] with A(f)* = D, f is a product of principal primes.