گراف اشتراكي ايده‌آل‌ سازي

Let R be a commutative ring with identity. The intersection graph of ideals of a ring R is an undirected simple graph denoted by Γ(R) whose vertices are one- toone correspodence with non- zero proper ideals an‎d two distinct vertices are joined by edge if an‎d only if the corresponding ideals of R have a non- zero intersection. Let M be a unitery R- module an‎d let RnM be the idealization of M in R. In this thesis, we investigate the interplay between the algebraic properties of RnM an‎d thegraph-theoretic properties of Γ(R nM). Under some conditions on the ring R an‎d the moduleM, we determine the exact form of ideals ofRnM an‎d characterize all rings R an‎d modules M for which Γ(R n M) is a star graph. Also, we give necessary an‎d sufficient condition on R an‎d M for which R n M is uniform an‎d then we conclude that when Γ(R nM) is a complete graph. Among other results, graph-theoretic properties of Γ(R nM) such as domination number, connectivity an‎d grith are obtained.

1404/09/16

ابراهيمي

79393