Almost b-Schreier domains

Almost Schreier domain is an extension of class of pre Schreier domains and b-operation is a type of star operation which is defined for an ideal A as an intersection of AV where V runs over all valuation over rings of the domain. Here we have studied a domain which is integrally closed and satisfies Almost Schreier property on its b-invertible ideals and call it an almost b- Schreier domain.