{"title":"Congruency, Homomorphism and Isomorphism on Autometrized Algebras.","authors":"Gebrie Yeshiwas Tilahun","doi":"10.12688/f1000research.159591.2","DOIUrl":null,"url":null,"abstract":"<p><p>This paper presents a study of congruence relations on autometrized algebras. We demonstrate that in a normal autometrized algebra, which satisfies certain conditions, the set of all congruence relations forms a complete sublattice within the set of all equivalence relations. Furthermore, we investigate the property that a congruence-permutable autometrized algebra is also congruence-modular. We also explore several fundamental properties related to congruence relations. Additionally, we introduce the kernel of a homomorphism and establish that it is a congruence relation. Lastly, we examine the homomorphism, isomorphism, and correspondence theorems of autometrized algebra using the concept of congruence.</p>","PeriodicalId":12260,"journal":{"name":"F1000Research","volume":"14 ","pages":"22"},"PeriodicalIF":0.0000,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12461190/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"F1000Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12688/f1000research.159591.2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/1 0:00:00","PubModel":"eCollection","JCR":"Q2","JCRName":"Pharmacology, Toxicology and Pharmaceutics","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents a study of congruence relations on autometrized algebras. We demonstrate that in a normal autometrized algebra, which satisfies certain conditions, the set of all congruence relations forms a complete sublattice within the set of all equivalence relations. Furthermore, we investigate the property that a congruence-permutable autometrized algebra is also congruence-modular. We also explore several fundamental properties related to congruence relations. Additionally, we introduce the kernel of a homomorphism and establish that it is a congruence relation. Lastly, we examine the homomorphism, isomorphism, and correspondence theorems of autometrized algebra using the concept of congruence.
F1000ResearchPharmacology, Toxicology and Pharmaceutics-Pharmacology, Toxicology and Pharmaceutics (all)
CiteScore
5.00
自引率
0.00%
发文量
1646
审稿时长
1 weeks
期刊介绍：
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