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
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: email@example.com)
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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, relationReferences:
- G. F. Birkenmeier, F. T. Mutlu, C. Nebiyev, N. Sökmez and A. Tercan, Goldie*-supplemented modules, Glasg. Math. J. 52 (A), 41–52, 2010.
- J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting modules: Supplements and projectivity in module theory, Basel, Birkhauser, 2006.
- F. Eryilmaz, Ss-lifting modules and rings, Miskolc Math. Notes 22 (2), 655–662, 2020.
- F. Kasch, Modules and rings, Published for the London Mathematical Society by Academic Press Inc. (London) Ltd., 372, 1982.
- E. Kaynar, H. Çalişici and E. Türkmen, Ss-supplemented modules, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 69 (1), 473–485, 2020.
- M. T. Koşan and D. Keskin, H-supplemented Duo modules, J. Algebra Appl. 6 (6), 965–971, 2007.
- A. Olgun and E. Türkmen, On a class of perfect rings, Honam Math. J. 42 (3), 591–600, 2020.
- D. W. Sharpe and P. Vamos, Injective modules, Lectures in Pure Mathematics University of Sheffield, The Great Britain, 190, 1972.
- Y. Talebi, A. R. M. Hamzekolaee and A.Tercan, Goldie-Rad-supplemented modules, An. Ştiinţ . Univ. “Ovidius" Constanţa Ser. Mat. 22 (3), 205–218, 2014.
- R. Wisbauer, Foundations of module and ring theory, Gordon and Breach, Philadelphia, 600, 1991.
- D. X. Zhou and X. R. Zhang, Small-essential submodules and morita duality, Southeast Asian Bull. Math. 35 (6), 1051–1062, 2011.