The residual of finitely generated multiplication modules (Q1063069)

Let R be a commutative ring with 1, and let A, B be any two ideals in R. It is known that if R is a Prüfer domain, then both \(A\cap B\) and [A:B] are finitely generated ideals. In this paper, several generalizations of these results to other classes of ideals and to modules are given (finitely generated projective ideals, finitely generated flat ideals, and finitely generated multiplication modules). The following is one of the main results: Let R be a commutative ring with 1, and let A, B be two f. g. multiplication ideals such that \(A+B\) is a multiplication ideal, and ann(B) is f. g. Assume that A, B, ann(B) can be generated by m, n, \(\ell\) elements, then [A:B] is finitely generated and can be generated by \(m(m+n)+\ell\) elements.