Institutional Repository UIN Sunan Kalijaga YogyakartaBEBERAPA SIFAT MODUL TEREDUKSI DAN REPRESENTASI GRAF ANNIHILATORNIM.: 22106010016Nisrina Rahadatul ‘AisyauthorLet MR be a module over a ring R with a unit. A module MR is defined as a reduced module if and only if, for every m 2 MR and a 2 R such that ma = 0, the intersection of the sets mR and MRa is singleton zero. A reduced module MR is a generalization of a reduced ring. A reduced module can be represented in the form of a graph called the annihilator graph. The set of vertices of the annihilator graph consists of the non-zero torsion elements of MR, where the connectivity of the vertices is determined by the annihilator and the residuals on the reduced module. This research not only discusses the definition of reduced modules and their representation in the annihilator graph but also the properties that arise in both. The annihilator graph of a reduced module is an undirected graph. Several examples of annihilator graphs of reduced modules are given, including incomplete graphs, complete graphs, and zero graphs (graphs consisting only of vertices with no connecting edges). An annihilator graph representation containing a cycle has a girth of only 3 or 4.510 Mathematics (Matematika)2026-05-13UIN SUNAN KALIJAGA YOGYAKARTA;FAKULTAS SAINS DAN TEKNOLOGIThesis

For work being deposited by its own author: In self-archiving this collection of files and associated bibliographic metadata, I grant Institutional Repository UIN Sunan Kalijaga Yogyakarta the right to store them and to make them permanently available publicly for free on-line. I declare that this material is my own intellectual property and I understand that Institutional Repository UIN Sunan Kalijaga Yogyakarta does not assume any responsibility if there is any breach of copyright in distributing these files or metadata. (All authors are urged to prominently assert their copyright on the title page of their work.)

For work being deposited by someone other than its author: I hereby declare that the collection of files and associated bibliographic metadata that I am archiving at Institutional Repository UIN Sunan Kalijaga Yogyakarta) is in the public domain. If this is not the case, I accept full responsibility for any breach of copyright that distributing these files or metadata may entail.

Clicking on the deposit button indicates your agreement to these terms.