Article ID: MTJPAM-D-22-00037

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)

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Abstract

In this study, it has been determined the notion of Goldie ss-supplemented modules by the help of the relation \beta_{{ss}}^{*}, which is defined in the form W\beta_{{ss}}^{*}Z, which provides conditions both of \frac{W + Z}{W} \subseteq \frac{\text{Soc}_{s}(A) + W}{W} and \frac{W + Z}{Z} \subseteq \frac{\text{Soc}_{s}(A) + Z}{Z} for submodules W and Z of module A is an equivalence relation. The main features of Goldie ss-supplemented modules provided by this relation is examined. It is shown that the epimorphism \gamma:A \longrightarrow B provided the relation \beta_{{ss}}^{*} under certain conditions and the relation \beta_{{ss}}^{*} , is expressed in the maximal submodules. In addition, we obtain notions of Goldie ss-lifting modules using the relation \beta_{{ss}}^{*} and we prove several properties of notions of these modules.

Keywords: Socle of a module, semisimple module, ss-supplement, relation \beta_{{ss}}^{*}

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