Title: Goldie ss-supplemented modules
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-22-00037; Volume 5 / Issue 1 / Year 2023, Pages 65-70
Document Type: Research Paper
Author(s): Fatih Gömleksiz a , Burcu Nişancı Türkmen
b
aGraduate School of Natural and Applied Sciences, Department of Mathematics, Amasya University, Amasya, Turkey
bFaculty of Art and Science, Department of Mathematics, Ipekköy, Amasya University, Amasya, Turkey
Received: 14 November 2022, Accepted: 10 May 2023, Published: 11 June 2023
Corresponding Author: Fatih Gömleksiz (Email address: action61@hotmail.com)
Full Text: PDF
Abstract
In this study, it has been determined the notion of Goldie ss-supplemented modules by the help of the relation , which is defined in the form
, which provides conditions both of
and
for submodules
and
of module
is an equivalence relation. The main features of Goldie ss-supplemented modules provided by this relation is examined. It is shown that the epimorphism
provided the relation
under certain conditions and the relation
, is expressed in the maximal submodules. In addition, we obtain notions of Goldie ss-lifting modules using the relation
and we prove several properties of notions of these modules.
Keywords: Socle of a module, semisimple module, ss-supplement, relation
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