http://digilib.uin-suka.ac.id/id/eprint/78383 2026-09-23T01:34:23Z info:eu-repo/semantics/descriptiveMetadata https://digilib.uin-suka.ac.id/id/eprint/78383/ BEBERAPA SIFAT MODUL TEREDUKSI DAN REPRESENTASI GRAF ANNIHILATOR Nisrina Rahadatul ‘Aisy, NIM.: 22106010016 510 Mathematics (Matematika) Let 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. 2026-05-13 Thesis NonPeerReviewed text id https://digilib.uin-suka.ac.id/id/eprint/78383/1/22106010016_BAB-I_IV-atau-V_DAFTAR-PUSTAKA.pdf text id https://digilib.uin-suka.ac.id/id/eprint/78383/2/22106010016_BAB-II_sampai_SEBELUM-BAB-TERAKHIR.pdf Nisrina Rahadatul ‘Aisy, NIM.: 22106010016 (2026) BEBERAPA SIFAT MODUL TEREDUKSI DAN REPRESENTASI GRAF ANNIHILATOR. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA. info:eu-repo/semantics/objectFile info:eu-repo/semantics/objectFile info:eu-repo/semantics/humanStartPage