{"title":"Classification of Dual Distributive Hyperidentities in Divisible Algebras","authors":"Yu. M. Movsisyan, S. S. Davidov","doi":"10.3103/s1068362324700225","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper provides a classification of nontrivial dual hyperidentities of the left and right distributivity satisfied in functionally nontrivial divisible algebras. If the nontrivial dual hyperidentities of the left and right distributivity hold in a functionally nontrivial divisible algebra, then the hyperidentity of the left distributivity is of rank two and is (equivalent to the hyperidentity) of the form</p><span>$$X(x,Y(y,z))=Y(X(x,y),X(x,z)),$$</span><p>while the hyperidentity of the right distributivity is the hyperidentity of rank two and is (equivalent to the hyperidentity) of the form</p><span>$$X(Y(x,y),z)=Y(X(x,z),X(y,z)).$$</span><p>For the classification of nontrivial hyperidentities of the left and right distributivity satisfying in functionally nontrivial <span>\\(q\\)</span>-algebras, see [1–4].</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3103/s1068362324700225","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper provides a classification of nontrivial dual hyperidentities of the left and right distributivity satisfied in functionally nontrivial divisible algebras. If the nontrivial dual hyperidentities of the left and right distributivity hold in a functionally nontrivial divisible algebra, then the hyperidentity of the left distributivity is of rank two and is (equivalent to the hyperidentity) of the form
$$X(x,Y(y,z))=Y(X(x,y),X(x,z)),$$
while the hyperidentity of the right distributivity is the hyperidentity of rank two and is (equivalent to the hyperidentity) of the form
$$X(Y(x,y),z)=Y(X(x,z),X(y,z)).$$
For the classification of nontrivial hyperidentities of the left and right distributivity satisfying in functionally nontrivial \(q\)-algebras, see [1–4].
期刊介绍：
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) is an outlet for research stemming from the widely acclaimed Armenian school of theory of functions, this journal today continues the traditions of that school in the area of general analysis. A very prolific group of mathematicians in Yerevan contribute to this leading mathematics journal in the following fields: real and complex analysis; approximations; boundary value problems; integral and stochastic geometry; differential equations; probability; integral equations; algebra.
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