Divisorial ideals and invertible ideals in a graded integral domain

摘要: Let R = Oapr R, be an integral domain graded by arbitrary torsionless grading monoid Z. In this paper we study v-ideals and invertible ideals of R. Section 3 determine necessary sufficient conditions for v-ideal to homogeneous whenever it contains a nonzero element. This condition is equivalent each Z finite type being equal xJ some x E R,, the quotient field J Either holds if integrally closed (but not conversely). special case that ‘-graded domain, u-ideal x.Z .Z only with respect positive degree. These results are then applied semigroup ring [X; r]. Our generalize work Querre [ 181 in polynomial case. 4 show many on u-ideals carry over ideals. 5 relationship between or If c inert extension, natural homomorphism $: Pic(R,) -+ HPic(R) isomorphism, where Picard group We investigate 4: + Pit(R) give