{"title":"Large-maximal small submodules","authors":"Wafaa H. Hanoon, Atwar A. Abboodi","doi":"10.47974/jim-1604","DOIUrl":null,"url":null,"abstract":"In this study, the ideas of Large-maximal small submodules and Large-maximal small radical of modules are presented. The primary attributes and features of the concept of large-maximal small submodules are provided. Additionally, we discuss the connections between this idea and various submodule kinds with the help of examples and observations that are relevant to our work. Where a proper submodule A of a T-module G is said to be Large-maximal small submodule, if A + B = G where B is a proper submodule of G, then B is Large-Maximal submodule of G. A Large-maximal small radical of module is the sum of all Large-maximal small submodule in G. It will be studied how this concept of radicality relates to other radical conceptions.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47974/jim-1604","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, the ideas of Large-maximal small submodules and Large-maximal small radical of modules are presented. The primary attributes and features of the concept of large-maximal small submodules are provided. Additionally, we discuss the connections between this idea and various submodule kinds with the help of examples and observations that are relevant to our work. Where a proper submodule A of a T-module G is said to be Large-maximal small submodule, if A + B = G where B is a proper submodule of G, then B is Large-Maximal submodule of G. A Large-maximal small radical of module is the sum of all Large-maximal small submodule in G. It will be studied how this concept of radicality relates to other radical conceptions.
本文提出了模的大-极大小子模和大-极大小根的思想。给出了大-极大-小子模块概念的主要属性和特征。此外，我们通过与我们的工作相关的例子和观察，讨论了这一想法与各种子模块类型之间的联系。其中t模G的真子模a是极大子模，若a + B = G，其中B是G的真子模，则B是G的极大子模。模的极大子模是G中所有极大子模的和。本文将研究这个根性概念与其他根性概念的关系。
期刊介绍：
The Journal of Interdisciplinary Mathematics (JIM) is a world leading journal publishing high quality, rigorously peer-reviewed original research in mathematical applications to different disciplines, and to the methodological and theoretical role of mathematics in underpinning all scientific disciplines. The scope is intentionally broad, but papers must make a novel contribution to the fields covered in order to be considered for publication. Topics include, but are not limited, to the following: • Interface of Mathematics with other Disciplines • Theoretical Role of Mathematics • Methodological Role of Mathematics • Interface of Statistics with other Disciplines • Cognitive Sciences • Applications of Mathematics • Industrial Mathematics • Dynamical Systems • Mathematical Biology • Fuzzy Mathematics The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Editor-in-Chief’s discretion. Special issue proposals in cutting-edge and timely areas of research in interdisciplinary mathematical research are encouraged – please contact the Editor-in-Chief in the first instance.
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