- M-cancellation Ideals
- P. NASEHPOUR ; S. YASSEMI ;
- Kyungpook mathematical journal, volume 40, issue 2, 2000, Pages 259~259
Abstract
Let R be a commutative ring with non-zero identy and let M be an R-module. An ideal α of R is called an M-cancellation ideal if whenever αP = αQ for submodules P and P of M, then P = Q. This notion is a generalization of the notion, cancellation ideal. We use M-cancellation ideals and a generalization of Dedeking-Mertens lemma to prove that for an R-module M with ZR(M)={0}, the following statements are equivalent :(i) Every non-zero finitely generated ideal of R is an M-cancellation ideal of R.(ii) For every f ∈ R[t] and g ∈ M[t], c(fg)=c(f)c(g)