Quasigroups, units and Belousov’s problem # 18
Închide
Conţinutul numărului revistei
Articolul precedent
Articolul urmator
650 0
SM ISO690:2012
KRAPEZ, Aleksandar, SHCHERBACOV, Victor. Quasigroups, units and Belousov’s problem # 18. In: Armenian Journal of Mathematics, 2019, nr. 9(11), pp. 1-27. ISSN 1829-1163.
EXPORT metadate:
Google Scholar
Crossref
CERIF

DataCite
Dublin Core
Armenian Journal of Mathematics
Numărul 9(11) / 2019 / ISSN 1829-1163

Quasigroups, units and Belousov’s problem # 18


Pag. 1-27

Krapez Aleksandar1, Shcherbacov Victor2
 
1 Mathematical Institute of the Serbian Academy of Sciences and Arts,
2 Vladimir Andrunachievici Institute of Mathematics and Computer Science
 
 
Disponibil în IBN: 4 octombrie 2019


Rezumat

We investigate {left, right, middle} units of quasigroups and families of identities which might imply their existence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov’s notions of left/right derivative operations for quasigroups. Partial solutions of the Belousov’s Problem # 18 and its generalizations are obtained. Several related problems remain open.

Cuvinte-cheie
Derivative operation, isotopy, loop, quasigroup, unit

Cerif XML Export

<?xml version='1.0' encoding='utf-8'?>
<CERIF xmlns='urn:xmlns:org:eurocris:cerif-1.5-1' xsi:schemaLocation='urn:xmlns:org:eurocris:cerif-1.5-1 http://www.eurocris.org/Uploads/Web%20pages/CERIF-1.5/CERIF_1.5_1.xsd' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' release='1.5' date='2012-10-07' sourceDatabase='Output Profile'>
<cfResPubl>
<cfResPublId>ibn-ResPubl-85204</cfResPublId>
<cfResPublDate>2019-06-11</cfResPublDate>
<cfVol>11</cfVol>
<cfIssue>9</cfIssue>
<cfStartPage>1</cfStartPage>
<cfISSN>1829-1163</cfISSN>
<cfURI>https://ibn.idsi.md/ro/vizualizare_articol/85204</cfURI>
<cfTitle cfLangCode='EN' cfTrans='o'>Quasigroups, units and Belousov&rsquo;s problem # 18</cfTitle>
<cfKeyw cfLangCode='EN' cfTrans='o'>Derivative operation; isotopy; loop; quasigroup; unit</cfKeyw>
<cfAbstr cfLangCode='EN' cfTrans='o'><p>We investigate {left, right, middle} units of quasigroups and families of identities which might imply their existence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov&rsquo;s notions of left/right derivative operations for quasigroups. Partial solutions of the Belousov&rsquo;s Problem # 18 and its generalizations are obtained. Several related problems remain open.</p></cfAbstr>
<cfResPubl_Class>
<cfClassId>eda2d9e9-34c5-11e1-b86c-0800200c9a66</cfClassId>
<cfClassSchemeId>759af938-34ae-11e1-b86c-0800200c9a66</cfClassSchemeId>
<cfStartDate>2019-06-11T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfResPubl_Class>
<cfClassId>e601872f-4b7e-4d88-929f-7df027b226c9</cfClassId>
<cfClassSchemeId>40e90e2f-446d-460a-98e5-5dce57550c48</cfClassSchemeId>
<cfStartDate>2019-06-11T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfPers_ResPubl>
<cfPersId>ibn-person-32288</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2019-06-11T24:00:00</cfStartDate>
</cfPers_ResPubl>
<cfPers_ResPubl>
<cfPersId>ibn-person-10569</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2019-06-11T24:00:00</cfStartDate>
</cfPers_ResPubl>
</cfResPubl>
<cfPers>
<cfPersId>ibn-Pers-32288</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-32288-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2019-06-11T24:00:00</cfStartDate>
<cfFamilyNames>Krapez</cfFamilyNames>
<cfFirstNames>Aleksandar</cfFirstNames>
</cfPersName_Pers>
</cfPers>
<cfPers>
<cfPersId>ibn-Pers-10569</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-10569-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2019-06-11T24:00:00</cfStartDate>
<cfFamilyNames>Shcherbacov</cfFamilyNames>
<cfFirstNames>Victor</cfFirstNames>
</cfPersName_Pers>
</cfPers>
</CERIF>