@phdthesis{digilib78383,
           month = {May},
           title = {BEBERAPA SIFAT MODUL TEREDUKSI DAN REPRESENTASI GRAF ANNIHILATOR},
          school = {UIN SUNAN KALIJAGA YOGYAKARTA},
          author = {NIM.: 22106010016 Nisrina Rahadatul ?Aisy},
            year = {2026},
            note = {Prof. Dr. Dra. Hj. Khurul Wardati, M.Si.},
        keywords = {Annihilator, Elemen Torsi, Modul Tereduksi, Residual, Graf Annihilator},
             url = {https://digilib.uin-suka.ac.id/id/eprint/78383/},
        abstract = {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.}
}